{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "49e806c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "4c04a1e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <style>\n",
       "        .output_wrapper, .output {\n",
       "            height:auto !important;\n",
       "            max-height:100000px;\n",
       "        }\n",
       "        .output_scroll {\n",
       "            box-shadow:none !important;\n",
       "            webkit-box-shadow:none !important;\n",
       "        }\n",
       "        </style>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#format the book\n",
    "import book_format\n",
    "book_format.set_style()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66a93043",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "\n",
    "考虑未来数据时，卡尔曼滤波器的性能不是最佳的。 例如，假设我们正在跟踪一架飞机，并且最新的测量值偏离当前轨迹很远，就像这样（为简单起见，我只会考虑 1 维）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "08448b81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "data = [10.1, 10.2, 9.8, 10.1, 10.2, 10.3, \n",
    "        10.1, 9.9, 10.2, 10.0, 9.9, 11.4]\n",
    "plt.plot(data)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('position');"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6afb355e",
   "metadata": {},
   "source": [
    "经过一段时间的接近稳定状态后，我们发生了非常大的变化。 假设变化超过了飞机飞行包线的限制。 尽管如此，卡尔曼滤波器还是根据当前的卡尔曼增益将新的测量值合并到滤波器中。 它不能拒绝噪声，因为测量可以反映转弯的开始。 诚然，我们不太可能如此突然地转向，但无法说是否\n",
    "\n",
    "* 飞机前段时间开始转弯，但之前的测量结果很嘈杂，没有显示出变化。\n",
    "\n",
    "* 飞机在转弯，这个测量噪音很大\n",
    "\n",
    "* 测量噪音很大，飞机还没有转弯\n",
    "\n",
    "* 飞机在反方向转弯，测量噪音极大\n",
    "\n",
    "现在，假设以下测量值是：\n",
    "\n",
    "    11.3 12.1 13.3 13.9 14.5 15.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c56816fc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2 = [11.3, 12.1, 13.3, 13.9, 14.5, 15.2]\n",
    "plt.plot(data + data2);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb776ae0",
   "metadata": {},
   "source": [
    "鉴于这些未来的测量，我们可以推断出是的，飞机开始转弯。\n",
    "\n",
    "另一方面，假设这些是以下测量。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "64251564",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data3 = [9.8, 10.2, 9.9, 10.1, 10.0, 10.3, 9.9, 10.1]\n",
    "plt.plot(data + data3);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6bf4a11b",
   "metadata": {},
   "source": [
    "在这种情况下，我们得出的结论是飞机没有转弯，而外围的测量结果只是非常嘈杂。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "294e0183",
   "metadata": {},
   "source": [
    "## An Overview of How Smoothers Work\n",
    "\n",
    "卡尔曼滤波器是具有马尔可夫特性的*递归*滤波器 - 它在步骤“k”的估计仅基于步骤“k-1”的估计和步骤“k”的测量。但这意味着来自步骤“k-1”的估计基于步骤“k-2”，依此类推回到第一个时期。因此，步骤“k”的估计取决于所有先前的测量值，尽管程度不同。 `k-1` 影响最大，`k-2` 次之，依此类推。\n",
    "\n",
    "平滑滤波器将未来的测量值合并到步骤“k”的估计中。 `k+1` 的测量将产生最大的影响，`k+2` 的影响较小，`k+3` 的影响较小，依此类推。\n",
    "\n",
    "这个话题叫做*smoothing*，但我认为这是一个误导性的名字。我可以通过低通滤波器来平滑上面的数据。结果将是平滑的，但不一定准确，因为低通滤波器将消除实际变化与消除噪声一样多。相比之下，卡尔曼平滑器是*最优的*——它们结合了所有可用信息来做出数学上可实现的最佳估计。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bda2ba19",
   "metadata": {},
   "source": [
    "## Types of Smoothers\n",
    "\n",
    "有三类卡尔曼平滑器可以在这些情况下产生更好的跟踪。\n",
    "\n",
    "* 固定间隔平滑\n",
    "\n",
    "这是一个基于批处理的过滤器。 此过滤器在进行任何估计之前等待收集所有数据。 例如，您可能是一位为实验收集数据的科学家，并且在实验完成之前不需要知道结果。 固定间隔平滑器将收集所有数据，然后使用所有可用的先前和未来测量来估计每次测量的状态。 如果您可以在批处理模式下运行卡尔曼滤波器，则始终建议使用这些滤波器之一，因为它会提供比前几章中滤波器的递归形式更好的结果。\n",
    "\n",
    "* 固定滞后平滑\n",
    "\n",
    "固定延迟平滑器会在输出中引入延迟。 假设我们选择 4 步的滞后。 过滤器将摄取前 3 个测量值，但不会输出过滤结果。 然后，当第 4 次测量进入滤波器时，将产生测量 1 的输出，同时考虑测量 1 到 4。 当第 5 次测量进入时，过滤器将产生测量 2 的结果，同时考虑测量 2 到 5。 当您需要最近的数据但可以承受一些延迟时，这很有用。 例如，也许您正在使用机器视觉来监控制造过程。 如果您能承受几秒钟的估计延迟，则固定滞后平滑器将使您能够产生非常准确和平滑的结果。\n",
    "\n",
    "* 定点平滑\n",
    "\n",
    "定点滤波器作为普通卡尔曼滤波器运行，但也会在某个固定时间 $j$ 产生状态估计。 在时间 $k$ 达到 $j$ 之前，过滤器作为普通过滤器运行。 一旦 $k>j$，过滤器估计 $x_k$，然后还使用 $j\\dots k$ 之间的所有测量值更新其对 $x_j$ 的估计。 这对于估计系统的初始参数或生成特定时间发生的事件的最佳估计非常有用。 例如，您可能有一个机器人在 $j$ 时间拍照。 当机器人继续移动时，您可以使用定点平滑器在 $j$ 时间为相机获取最佳姿势信息。\n",
    "\n",
    "## Choice of Filters\n",
    "\n",
    "这些过滤器的选择取决于您的需求以及您可以节省多少内存和处理时间。 定点平滑需要存储所有测量值，并且计算成本非常高，因为每次测量都会重新计算每个时间步的输出。 另一方面，滤波器确实为电流测量产生了不错的输出，因此该滤波器可用于实时应用。\n",
    "\n",
    "固定滞后平滑只需要您存储一个数据窗口，并且处理要求适中，因为每次新测量只处理该窗口。 缺点是滤波器的输出总是滞后于输入，并且平滑不如固定间隔平滑那样明显。\n",
    "\n",
    "固定间隔平滑以必须进行批处理为代价产生最平滑的输出。 大多数算法使用某种前向/后向算法，其速度仅为递归卡尔曼滤波器的两倍。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "118a385f",
   "metadata": {},
   "source": [
    "## Fixed-Interval Smoothing\n",
    "\n",
    "文献中有许多可用的固定滞后平滑器。我选择实现 Rauch、Tung 和 Striebel 发明的平滑器，因为它易于实现且计算效率高。它也是我在实际应用中最常使用的平滑器。这种平滑器通常称为 RTS 平滑器。\n",
    "\n",
    "RTS 平滑器的推导运行到几页密集的数学。我不会把它强加给你。相反，我将简要介绍算法、方程，然后直接进入平滑器的实现和演示。\n",
    "\n",
    "RTS 平滑器的工作原理是首先以批处理模式运行卡尔曼滤波器，计算每一步的滤波器输出。给定每个测量的过滤器输出以及对应于每个输出的协方差矩阵，RTS 向后运行数据，将其对未来的知识整合到过去的测量中。当它到达第一次测量时，它就完成了，过滤后的输出以最大优化的形式合并了所有信息。\n",
    "\n",
    "RTS 平滑器的方程非常简单易行。此推导适用于线性卡尔曼滤波器。 EKF 和 UKF 也有类似的推导。这些步骤是在批处理的输出上执行的，从最近的时间倒退到第一个估计。每次迭代都将未来的知识合并到状态估计中。由于状态估计已经包含了所有过去的测量结果，因此每个估计都将包含过去和未来所有测量的知识。区分过去、现在和未来非常重要，因此我使用下标来表示数据是否来自未来。\n",
    "\n",
    "Predict Step\n",
    "    \n",
    "$$\\begin{aligned}\n",
    "\\mathbf{P} &= \\mathbf{FP}_k\\mathbf{F}^\\mathsf{T} + \\mathbf{Q }\n",
    "\\end{aligned}$$\n",
    "\n",
    "    Update Step\n",
    "    \n",
    "$$\\begin{aligned}\n",
    "\\mathbf{K}_k &= \\mathbf{P}_k\\mathbf{F}^\\mathsf{T}\\mathbf{P}^{-1} \\\\\n",
    "\\mathbf{x}_k &= \\mathbf{x}_k + \\mathbf{K}_k(\\mathbf{x}_{k+1} - \\mathbf{Fx}_k) \\\\\n",
    "\\mathbf{P}_k &= \\mathbf{P}_k + \\mathbf{K}_k(\\mathbf{P}_{k+1} - \\mathbf{P})\\mathbf{K}_k^\\mathsf{T}\n",
    "\\end{aligned}$$\n",
    "\n",
    "As always, the hardest part of the implementation is correctly accounting for the subscripts. A basic implementation without comments or error checking would be:\n",
    "\n",
    "```python\n",
    "def rts_smoother(Xs, Ps, F, Q):\n",
    "    n, dim_x, _ = Xs.shape\n",
    "\n",
    "    # smoother gain\n",
    "    K = zeros((n,dim_x, dim_x))\n",
    "    x, P, Pp = Xs.copy(), Ps.copy(), Ps.copy\n",
    "\n",
    "    for k in range(n-2,-1,-1):\n",
    "        Pp[k] = F @ P[k] @ F.T + Q # predicted covariance\n",
    "\n",
    "        K[k]  = P[k] @ F.T @inv(Pp[k])\n",
    "        x[k] += K[k] @ (x[k+1] - (F @ x[k]))     \n",
    "        P[k] += K[k] @ (P[k+1] - Pp[k]) @ K[k].T\n",
    "    return (x, P, K, Pp)\n",
    "```\n",
    "\n",
    "此实现反映了 FilterPy 中提供的实现。 它假设卡尔曼滤波器以批处理模式在外部运行，状态和协方差的结果通过 `Xs` 和 `Ps` 变量传入。\n",
    "\n",
    "这是一个例子。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6ec66f18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from numpy import random\n",
    "from numpy.random import randn\n",
    "import matplotlib.pyplot as plt\n",
    "from filterpy.kalman import KalmanFilter\n",
    "from filterpy.common import Q_discrete_white_noise\n",
    "import kf_book.book_plots as bp\n",
    "\n",
    "def plot_rts(noise, Q=0.001, show_velocity=False):\n",
    "    random.seed(123)\n",
    "    fk = KalmanFilter(dim_x=2, dim_z=1)\n",
    "\n",
    "    fk.x = np.array([0., 1.])      # state (x and dx)\n",
    "\n",
    "    fk.F = np.array([[1., 1.],\n",
    "                     [0., 1.]])    # state transition matrix\n",
    "\n",
    "    fk.H = np.array([[1., 0.]])    # Measurement function\n",
    "    fk.P*= 10.                     # covariance matrix\n",
    "    fk.R = noise                   # state uncertainty\n",
    "    fk.Q = Q_discrete_white_noise(dim=2, dt=1., var=Q)  # process uncertainty\n",
    "\n",
    "    # create noisy data\n",
    "    zs = np.asarray([t + randn()*noise for t in range (40)])\n",
    "\n",
    "    # filter data with Kalman filter, than run smoother on it\n",
    "    mu, cov, _, _ = fk.batch_filter(zs)\n",
    "    M, P, C, _ = fk.rts_smoother(mu, cov)\n",
    "\n",
    "    # plot data\n",
    "    if show_velocity:\n",
    "        index = 1\n",
    "        print('gu')\n",
    "    else:\n",
    "        index = 0\n",
    "    if not show_velocity:\n",
    "        bp.plot_measurements(zs, lw=1)\n",
    "    plt.plot(M[:, index], c='b', label='RTS')\n",
    "    plt.plot(mu[:, index], c='g', ls='--', label='KF output')\n",
    "    if not show_velocity:\n",
    "        N = len(zs)\n",
    "        plt.plot([0, N], [0, N], 'k', lw=2, label='track') \n",
    "    plt.legend(loc=4)\n",
    "    plt.show()\n",
    "    \n",
    "plot_rts(7.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4da1935c",
   "metadata": {},
   "source": [
    "我在信号中注入了大量噪声，让您可以直观地将 RTS 输出与理想输出区分开来。 在上图中，我们可以看到，绘制为绿色虚线的卡尔曼滤波器与输入相比相当平滑，但是当连续的多个测量值偏向线的一侧时，它仍然偏离理想线 . 相比之下，RTS 输出既极其流畅，又非常接近理想输出。\n",
    "\n",
    "有了可能更合理的噪声量，我们可以看到 RTS 输出几乎位于理想输出上。 卡尔曼滤波器输出虽然要好得多，但变化量仍然要大得多。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cba563c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(noise=1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f541f650",
   "metadata": {},
   "source": [
    "但是，我们必须明白，这种平滑是基于系统模型的。 我们已经告诉过滤器，我们正在跟踪的内容遵循具有非常低过程误差的恒定速度模型。 当滤波器*向前看*时，它会看到未来的行为与恒定速度非常匹配，因此它能够拒绝信号中的大部分噪声。 假设我们的系统有很多过程噪声。 例如，如果我们在阵风中跟踪一架轻型飞机，它的速度会经常变化，过滤器将无法区分噪音和风引起的不稳定运动。 我们可以在下图中看到这一点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "797c92df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(noise=7., Q=.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7bc84cee",
   "metadata": {},
   "source": [
    "这强调了这样一个事实，即这些过滤器不会*平滑*该术语口语意义上的数据。 滤波器根据之前的测量结果、未来的测量结果以及您告诉它的有关系统行为和系统中的噪声和测量结果做出最佳估计。\n",
    "\n",
    "让我们通过查看卡尔曼滤波器与 RTS 平滑器的速度估计来总结一下。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1aebd627",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "gu\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_rts(7.,show_velocity=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb5c9135",
   "metadata": {},
   "source": [
    "作为隐藏变量的速度的改进更加引人注目。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0ee52f4",
   "metadata": {},
   "source": [
    "## Fixed-Lag Smoothing\n",
    "\n",
    "如果您可以在批处理模式下运行，上面介绍的 RTS 平滑器应该始终是您的算法选择，因为它将所有可用数据合并到每个估计中。 并非所有问题都允许您这样做，但您可能仍然对接收先前估计的平滑值感兴趣。 下面的数字线说明了这个概念。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f2a88c8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QW7gGEAAAwDEEQAAAAMcQAAEAABxDAAQAAHAMARAAAMAxBEAAAADHEAABAAAcQwAEAABwDAEQAADAMQRAAAAAxxAAAQAAHEMABAAAcAwBEAAAwDEEQAAAAMcQAAEAABxDAAQAAHAMARAAAMAxBEAAAADHEAABAAAcQwAEAABwDAEQAADAMQRAAAAAxxAAAQAAHEMABAAAcAwBEAAAwDEEQAAAAMcQAAEAABxDAAQAAHAMARAAAMAxBEAAAADHEAABAAAcQwAEAABwDAEQAADAMQRAAAAAxxAAAQAAHEMABAAAcAwBEAAAwDEEQAAAAMcQAAEAABxDAAQAAHAMARAAAMAxBEAAAADHEAABAAAcQwAEAABwDAEQAADAMQRAAAAAxxAAAQAAHEMABAAAcAwBEAAAwDEEQAAAAMcQAAEAABxDAAQAAHAMARAAAMAxBEAAAADHEAABAAAcQwAEAABwDAEQAADAMQRAAAAAxxAAAQAAHEMABAAAcAwBEAAAwDEEQAAAAMcQAAEAABxDAAQAAHAMARAAAMAx/w9+SwUJSb/UcAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from kf_book.book_plots import figsize\n",
    "from kf_book.smoothing_internal import *\n",
    "\n",
    "with figsize(y=2):\n",
    "    show_fixed_lag_numberline()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21e51b7d",
   "metadata": {},
   "source": [
    "在步骤 $k$ 我们可以使用正常的卡尔曼滤波器方程估计 $x_k$。 但是，我们可以通过使用收到的 $x_k$ 测量值对 $x_{k-1}$ 做出更好的估计。 同样，我们可以通过使用对 $x_{k-1}$ 和 $x_{k}$ 的测量结果对 $x_{k-2}$ 做出更好的估计。 我们可以将此计算扩展回任意 $N$ 步。\n",
    "\n",
    "这个数学的推导超出了本书的范围。 如果您有兴趣，Dan Simon 的 *Optimal State Estimation* [2] 有一个很好的说明。 这个想法的本质是，我们不使用状态向量 $\\mathbf{x}$，而是创建一个包含以下内容的增强状态\n",
    "\n",
    "$$\\mathbf{x} = \\begin{bmatrix}\\mathbf{x}_k \\\\ \\mathbf{x}_{k-1} \\\\ \\vdots\\\\ \\mathbf{x}_{k-N+1}\\end{bmatrix}$$\n",
    "\n",
    "这会产生一个非常大的协方差矩阵，其中包含不同步骤状态之间的协方差。 FilterPy 的类“FixedLagSmoother”会为您处理所有这些计算，包括创建增强矩阵。 您需要做的就是像使用“KalmanFilter”类一样组合它，然后调用“smooth()”，它实现了算法的预测和更新步骤。\n",
    "\n",
    "每次调用“smooth”都会计算当前测量的估计值，但它也会返回并调整之前的“N-1”点。 平滑后的值包含在“FixedLagSmoother.xSmooth”列表中。 如果您使用“FixedLagSmoother.x”，您将获得最新的估计值，但它没有经过平滑处理，并且与标准卡尔曼滤波器输出没有区别。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b361c498",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard deviation fixed-lag: 2.616\n",
      "standard deviation kalman: 3.564\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_30877/221685323.py:39: UserWarning: marker is redundantly defined by the 'marker' keyword argument and the fmt string \"o\" (-> marker='o'). The keyword argument will take precedence.\n",
      "  plt.plot(zs,'o', alpha=0.5, marker='o', label='zs')\n"
     ]
    },
    {
     "data": {
      "image/png": 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4w1d/4LuS7wA4PfV0bh57M+D5sDU0eihDo4dy85ibya3OZeW+lazKX0VeTR4JoYdTOcpt5XxZ+CVnpJ1BpCkyEC/lhJxuJwcbDlLRUEFGVAZGrRGA5XuX8789/6O8oZzyhnIqGypxqYfP12ExwxgU4QmGZ/afSbQpmvEJ4xmXMI7YkFi/tllRFEL1hz/k6jQ6zht8Hp/v+5zC+kJe3P4iL25/keHRwzl70NmcPehsv7fJHyRYF8KP3G5VylOJLpFSdb2DvI8912d7P+PBDQ9S56gjRBfCHSfdwcUZF7ebWqEoChlRGWREZbBozCLyqvOIC41rWb9y30oe+e4RHlQeZGLSRGb2n8mMfjOIMkV150tqYXPaeH7r83xV/xWvLnuVg/aDVNmrWtJW3j33XYZGDwWgoL6AtQVr2+wjwhBFfEgSeRXlDLAMRKNRmDVgFrMGzOrOl9LKoIhB/OXUv/DHk//I2v1f8L+8j/m6eAM7K3eys3In/Q/uZ5ohFmwHD980Orj43wFrc0fIXwch/ESqeAhvSJ323uHo9/FI8j4Gr7d+fouHNj4EQFZsFv936v8xIGJAh58/OHJwq8cRxgiGRg1lV9Uuvin6hm+KvuEvG//CzWNuZmHmQjRK91bS/tumv/H27rc9D6oPL9cpOmJCYlqllkxJnkK4IZy4kDjiQuOot4bwXa6T/Ao7dmsTn23SsntfXvf9b3NYoWofVO+D6gNgLfcE3Q2VhwLwSkJsB5lrO8jcJgdVGg0rwkJZGxrClDWPt+zmhchwcvR6/lDnIDAfmTpOgnUh/ECqeAhvHV2qLinCRIhBS4OjieIau0zN3UMcq+Rgha2SsvpGIkN1jBsUQbGtCLfbTZPahElnIjEssWUfPx38CafbiVt1t9SijjRGEhMSQ4QxotsDvb5gzsA5vLzjZc4dfC7Xj7re60oj5ww6h3MGnUN+TT6f7/+cFfkr+LnyZ57c8iTfFn/LszOexaA1+Kj1J7Zo7CJ+OvgTg2yDmDlpJkmWJOJC44g0RrY5n4bHDGd4zHDA87/tv1v8/L+tyQk1BZ5gvCr/cGDe/NNa3qndRSl6LlciuJxoGDgCQmNQQ6L5oPprGnBjmfo7UFUI4otRJVgXwsekiofwFV/UaReBlx5vYcEp/Vi1o7yl5OCG2ptQcUM9rFzbevuTk07mxVkvtjy+dsW11Dvr29338OjhvH3u2y2Pn9z8JCoqMaYYYkNiiQmJabkfbgzv0YG9qqr8dPAnlu1dxnfF3xFmC+MszvLJvh1NDj7b+xnnDT4PRVGIMEbwwfkfEKLz7TceAyIGcF3WdVybeS0f5H7AI989Qpolze+But1lZ9W+VZw7+FwAok3RvDrrVT777DOmJE9Brz/xhxGf/W9z2KCu2HOrLToUhOd7flbtg9oCUN3Hb4wpAiL7Q2Q/MCdAaMwRt+hDt0OP9aFtA3FV5YnKnRTXF6PrP+OErz3QJFgXwsekiofwJZmau+dyup2sL1jPhzkfggJPTXu6peTgP11aXKobjaJBo2jQKtqWnyadqdV+ksxJ2Jy2lvUqKtWN1dQ01rTJeX5799vUOerabc+ImBG8dc5bLY+PnKSmu3TlOp686jyW7V3G8r3L2V+3v2X5EN2QVtvd8+U99Avvx7j4cWTFZXU40M6pyuHuL+9mV9Uu3KqbCzIuAPB5oH4kRVG4MONCxsaPbfUtSrW9mhB9SMvFnb6wr3Yft6+9nV1VuwBaAvbOljU80f+25HAd5YV7KP+5lASlEupKPMF4XQnUNf8sBnvNiQ+mNUJUf09A3t7PEO8SVxRFYUTMCEbEjPBqP91FgnUhfEyqPwhf60qddhE4uVW5fJj7IZ/s+YRKeyXgqTFd7agiNcpCchh8O+cbjAZjhwKm9897v93lziZnqxkgVVXlmsxrONhw0FPVw17huW8/6AnsjYcDHKfbyaWfXMopyaewMHNht1TI6Mp1PDevvpl1BetaHpu0JqalTePUpFPZv/1w4F5qLeWTPZ+0PNYpOobHDGdc/DjGJoxlbPzYNmUB3aqb1396nae2PIXD7SDadOzSgf4yMGJgq/bcsf4OquxVPHraoz4pN7hq3yr+9PWfsDqtRJuivXqfm/+3xVFP6sFskuqyibLlY3ZUYHaUEeqsREGF3A7sTB8KliQIT/aMjkcNaB2QmxNA03O/BfI1CdaF8DGp/iCClaqq/PHrPzKz/0ympU0LdHN6nS/2f8FL219iW8W2lmUxphjOSz+PeenziDZF43Q6AdBqtF5P2KLX6onQRrQ8VhSF67Kua3fbowP79QfWk1udS251Lm/teotLhlzCNZnXtKpg4ksduY4nwmzn8/2fc/GQi1tyxAdFDOLroq+ZkjyFuQPnMj1tOqH6UJxOJ8t2LmvZv0ln4g+T/sCWsi1sKd1Cqa2U7RXb2V6xnVd/epXLhl7GH0/+Y0tfbC3fygvbXmBj8UYATks9jftPuT+gZf0K6grYXbWbSnsll316GXdNvIuLMi7q0nnibHLyxOYneH3n6wCMix/Ho6c9SkJYwgmeefSOGqD4Ryj4nn57NvKX/I1EucqOuXkTWlRzArqIZLAkeoJxSyJYjnpsDA/qHPFgI9GCCFo9teyhVPEQwWBvzV7e3uVJiXjoVE9VixX5K/g472M+zvuYaanTuGviXaRaUgPc0p6r+YJPvdYTWFbYK9hWsQ2douO01NO4IOMCpqRMCYpp0I8O7M/odwbPzniW5398nm0V23h95+u8s/sdLh5yMddkXkN8aLzPjn28XGe9voHvylZx85pNFDt24FbdpFnSODXlVMAzGc61WdcSYYw43iGIMEZw+bDLuXzY5Z6/s9ZitpRt4YfSH9hStoXxCeNbts0+mM01K64BPCP1d5x0B5cMuSTgs132C+/Hu+e+yz1f3cOG4g3c/+39fFP0DfdOvveEr/9IxfXF/G7979hW7vnQuDBzIb8Z+xt0mhOEfKoKlXugYBMUboKC76FkO7g93wKHHrq50VAROpgSSxblYUOoM8ZTr49le20o/fv158ZpGdAD/lf3JBKsi6DUk8seShUPEShOt5O1B9by1q63WkYMNYqGm8feTGJYIqelnsY1mdfw2o7XWFuwlm+Lv+X6Uddz9ciru7USRU9XXF/MR3kf8WHuh1w98mouH3Y5AHMGzMHmtPWIiVcURWFq6lROTTmVb4u+5bkfn2Nr+Vbe2PkG7+x6h4/mfeSzD3JH5zq73I3ss3/HnoYvKWz8ETcuaPRsOypuVKuLYGNCYrr02pLNySSbkzln0Dlt1h+oO4BRa2REzAjuP+X+Vqko3aahGg7mgtMGTju4GsBpJ85l54Xw8bza2MTTlZtYtW8V2Qe+4pGw4YzD5NnO1egZ8W5ygNbgSSkxhII+BPRh5DbVsK1yGxaNgb+kzGa6Ngl+/p9nO/2h7QxhgJa42mw0X+2Eoi2e4Lyhsm1bzQmQehKkTqAgbCT/yougxK5r+78twsCszCT53+YHEqyLoNMbyh72pioePfUbjr6k1FrKeznv8e7udylv8JQ1U1A4LfU0Lh16KXEhcbjdKgfrYG7KtUyMnclLO59gU+n3PPPDM3yS9wl3T7qbU5JPCfArgaL6InKrc6lprKHWUUttYy01jhpqGj23O0+6s1P1rn2poqGCv2z4C6v3r26ZPGZF/oqWYN1isBxzWvRgpSgKp6ScwuTkyWwo3sDzPz6PTqNrFajbnLZWs0R2hqPJwdaybVQ4C0k2ZHr2565iXfWTLdtE6foT4T6J3025jNMHDfPq9XTEeYPP49xB53bfSHqTC8p2eILhgs2eUeuK3cfcXAMsBE4yGLgzPoYDenjw4AbeLSyhI5cDTwX+bAljcoOd1Lwlx9xOD5wCkHfEQq0Bksa0BOekToCItJaUlVTgypS6XvG/rSfpcrC+fv16HnvsMTZv3kxxcTEffPAB8+bNa1l/9dVX8+qrr7Z6zuzZs1m+fHmXGyt6v95U9rA3VPHoyd9w9CVrDqzhuR+fAzwl2S7KuIiLh1xMsjkZaP99HB97N1NHb+M/u/9Bfm0+j33/GO+e+67fqoMcqD3A5/s/Z8fBHS2Bd62jlprGGl6e8zLDoj1B2rK9y3hqy1PH3M+CkQsCEqx/Xfg193x1T8sFoxMTJzIvfR5n9j+z29viD4qiMDl5MicnnYzVaW1ZfrDhIOd+eC6zB8zmuqzrSDGnHHMfqqpSUFfAtoptnnzx8u3srNyJ0+0kXjOBdMcwLCY9Fm0CCYbhJBlGMjDkVHRNiVTbnAyK7Oe7F6Sq0FgLtcWHywTWFbc8VupKPKPLUf2PuLjx0M+w2K7nU6sq1BZ6UkkKvofCzVC01TMifrTwFDBaQGfyjHbrjKALAb0JdCFk6oy8o9XzV+vPzE8aiXZEUqv1aPXQ5KTCVsZDhSu4I3IcKWjBaeMSp81TItHZfGvwTCbkbDh0s6I6G7BpLIRknIam3yRImQCJmZ52HEdv+N/W03Q5WLdarYwePZprrrmGCy+8sN1t5syZw8svv9zy2Gj0XSki0Tv1trKHPbmKR2/4hqM3qmms4cPcD0k2JzOz/0wAzh10LusOrOP89PM5s9+ZLTnUcOz3cUdxLdG1Q3hyylKWF77Gmf3PbAnUnU1OUPBZrvU/t/2TZ3545rivqVlyWDLDo4cTYYwgwhhBuCHcc9/geTwgfEDLti9tf4npadPbzBbpa6/teI3HNj0GQEZUBo9MfYQhUUNO8KyeSVEUzAZzy+PV+1dT56jj3d3v8mHOh5yffj7XZV1HqiUVZ5Oz5Vxzq25mvTuLUltpm31GGiOJ0oVTXGNvuY7n7FjPdRSqqpJTWd+563hUFWoKiK7fjbLTCdayIwLyI8oFHvGh45j2trNMH9Z+ucDmYN54uH9orIeiHw7leB+61Ze03acxAlLHewLi1AmQMt7zoeAEwoAHjlr21s9vER0Sycz+M/m+5HvuWLeEg/aD1Jnj+Nfsf534NR/icjr5fNkyzjrrLDQdqLN+pGD439aXvvXtcrA+d+5c5s6de9xtjEYjiYmJx93mSI2NjTQ2NrY8rq2tBcDpdLZcQd+dmo8ZiGP3Fp3twxqrHZvDSWK4AfehmfqOZNIpNDhc1FjtJFoCf9FWdwjEeeh2qyzbVkRFnZ2M+LBDH5zchBk0DI4NIafMymfbirh+6sAe88exp/8+F9YX8s/t/2Tl/pU0NjUyNGoopyedjqIoGBUjz0w7FAy7Pbnr0LH3cf3OWm6dehsajdLSN//a8S+W5y/n9yf9nvHxhy/MO1EfqqpKTnUOqw+s5vSU01tqGI+MGolW0TIufhxTkqcQY4ohwhBBuDGcCEMEiWGJLfucmTaTmWkzj9sXTqeTLw58wVNbnuL5H5/n9nG3c1F616pmdMTY2LHoNXouGHwBt469FZPO1OXzqKedhxcMuoD+5v68mP0iG0s28l7Oe3yY+yEp5hRCdCH8d+5/W7aNC4mj0l7J0KihZMVkkRmbSWZMJqnmVPLKrby2YT+7SmoPfWjUYjviOp7pQ2JoanLRdPSffVWFuiKUoq0oxVtRin9AKd6K3l7NVICc47dfNUWAORHVkgSWRFRzEliSUM3x4KhHqd6HUr0fqvehVO+DuhIUpxXKfvLc2ttnaAxqRD+UJgeU70Q5agIfVdFC/AjcKRNQU8ajJo+HmMFw9IRUXTgHcqpzeOT7R3C5XZyceDLflX6HW3WTHpHOXePv6tR51dPOxSPlltWzamcZe8qtLd8WDooLY+bweNLjzSfegY9424cdfZ6iqqrapSMcuRNFaTcN5sMPP8RgMBAVFcUZZ5zBQw89REzMsS8Wue+++7j//vvbLF+6dCmhoT1zdFJ0zkE7LDugwawDUzsfJRtcYHXBWWluYkxt1wvfkPchuPzo+JGPbR/TeOgqvCRtEhMNExlvGH/cGSm78j66VBd/r/07NapntHu0fjRzQuZg0bT/LYqqqhQ1FbHDuYMdzh0cdB8EYLJhMmeHng1Ak9qEzW3H4QyjsQmMWogyelcwos5dx3u298h1eYo6D9cP54KQCwjVeP+/QlVVyt3lxGsPV0SpaqoiSuvdRCw93X7XftbY17T0uQYNf4z4IwbFc3Fytbsas2JGp7Q/Dlhig22VCqUNCi436DSQGKKSFa2SeOhtMzpriLTtJdK259DPfEyutpPouBUtDfpo7PpI7PooGvRR2I+8GaKw6yJp6uTkQhq3kxBHBaGOcsIaywl1lLe6b2hqO1pv00dTFTaYqtDBVIUNpiZ0AE0a/2QSNKlNrLav5svGL1uumxirH8u5oee2vA+9XYkN1pUoWJ0KUQYwaMHRBFUOCNOrnJ54+HwKdjabjfnz51NTU0N4ePgxt/NbsP7mm28SGhrKwIEDycvL45577sFsNvPtt9+i1bafE9neyHpaWhoVFRXHfRH+4nQ6WbVqFTNnzuzQVLyirc72odut8sKXe9lRVHvESKCHqqrklFnJTA7vUSO63grEebirpI5/rM1jUGwY2nb6ucmtsrfCxqJpgxia2DNSYXri77PNaePRzY/y8Z6PARgTN4Zbx95KVkxWh0aRu/o+1jTW8I8f/8H7ue+jomLWm7lp1E3MGziPNZ+vYebMmbgUF8/++CxrCtZQbC1uea5BY+CU5FM4d+C5TE+bDvhvFMytuln681Ke/vFpXG4XcSFxPHTKQ5yUcFKX91nvrOfh7x5m1YFVvDrrVYZHD+/yvtrTE8/Do+2q2kVFQwUjoke0mUH1RNxulaIaO9ZGFxa1jiTrz2hLf/SMmhf9gFJX1OY5zSPVatJo1KQxuJPG4IzKYNWadd3fj/baQ6Pw+0FRUJPHeib36WYbSzby2s7XmN1/NucNOq9L++iJ52KwxQje9mFtbS2xsbEnDNb9Vg3m8ssvb7mflZXFqFGjGDx4MGvXrmXGjBntPsdoNLab167X6wN6IgX6+L1BZ/rwrFHJlNY5yKtoaFMaKtZiYu6oZIzGvjGCcKTuPA8jwkyEGvTYXSqWdoZkrQ4nIQYdEWGmHve70ZN+n38o+YGP93yMRtFw/ajruWHUDSeulXyErr6PsfpY7ptyHxcPvZgHNzzITwd/4tHNj7KucB1nus9Er9cTogthdcFqSqwlhOhCmJoylZn9ZzI1dSph+rCWfeWW1fH6dwVH5MzrsDlc7Cypp7TO4fW1DwtHLeTklJO5c/2d5Nfmc+PqG/nNuN8cc3Kg49lWvo07199JYX0hWkXLrppdjEoY1eW2HU9POg9baawns2QnVOZB7pfgdnqqnbid0ORs57GrzfKBTU6wHYTqfe0cQIG4oZA8FpLHQfJYlMRM0IfQHHppoSWFpNv7UR8DlhhIG9d9x2zHqWmncmraqT7ZV086Fw9U2sg/2EBKVChabdu/aSlRoew92ECZ1dWtOfVd7cOOPqfbSjcOGjSI2NhYcnNzjxmsCwG9q+xhTyUTOwWHaWnTuH7U9ZycdDInJXZ+tNjb9zEzNpOlZy3l3d3v8tQPT7Grahdnmc4CPN+o/nbcbwnRhnBKyimE6Nruo7uqOw2PGc5b57zFX7//K+/nvM+giM5N0+5W3fw7+98s+WEJLtVFclgyfz3tr4yJH9PlNvUqTU7IXQ3b34FdyzzVRXwlelBLUE7yWEga5amQIkQ7rA4XdlcToYb2/2aFGLSU1tqxOlzd3DL/6rZgvaCggIMHD5KU1P1fF4meR0pDBZZM7BQYlfZKHv/+cRZPWNwyqc4tY2/p8v588T5qNVouG3YZZ/Y/k39t/xfVBdUt69qbcOZI3VndKVQfyv2n3M/lQy9neMzh1JUSawmJYccudFBmK+Oer+5pmURqzoA5/Gnynwg3+DH1UnWDyw5uuycQbhl57uB9VIgfATHp/puyXVXhwEbY9jbs+KD1ZDnRg2DgaaA1esoHanSHfupBqzv089DyY60zmD1lAkP69nUAonPCDDpMOi02hwuLqe2odIOjCaNOS5ihd00j1OVXU19fT25ubsvjvXv3snXrVqKjo4mOjub+++/noosuIjExkby8PO68807S09OZPXu2Txouer9gKA3Vl8k3HN1rQ/EG7v7ybioaKqhz1PHMjGOXOuwMX72PMSEx3Db2NpYVL+vwsQMxCnZ0oH7xJxdzasqp/HHSH1uVJGy2Mn8lG4s3EqIL4e6JdzMvfZ7/JsvJ/xrt2oc5P/9L2OqD/YVEHZq8ZiKkneQpB+jtqHTZTs8I+vZ3oHr/4eVh8ZB5EYy6xDMS3l0TCglxhL76rW+Xg/VNmzYxffr0lseLFy8GYMGCBTz33HNs27aNV199lerqapKTk5k1axYPPvig1FoXfU5edR7lDeWcnHRyoJvSafINh/853U6W/LCEf2f/GxWVwRGDuWVc10fT2xOo9zHQo2CbSjdR76jnf3v+x9ayrfz1tL8yOm50q23mD59PYX0hlwy9pNPpMx2W/zWsfRjyv+SYtXu0hsOjz+3e1x8eoXY7oXQHNFRBzkrPDTylAeNHeAL4tImeID5m8IkD65pCyH4Xtr0DpdsPLzeYYfi5kHUJDDzd0x4hAqivfuvb5d+8adOmcbxCMitWrOjqroXoNSoaKvjFZ79Ao2h4/7z3iQ+NP/GTgox8w+E/B+oOcNf6u9he4QmQLhlyCXecdEe7+d/eCsT7GOhRsHMGnUOqOZW71t9FYX0hCz5bwDWZ17Cvdh8PTnmQUH0oGkXDXRPv8svxjwzSAdDoaRpzJV80jOD0sy5Gbwr1BN8abedHql0OT2B94DvPreB7qDkApdme2+ZDExKGRB8K3g+NwKeM90zq01AFP30E29+F/K/gUBlANHrImAlZF8OQuWCQ330RXPrit77yMVkIP/rbpr9R56jjlORTiAuJC3RzRBDZWraVGz+/EavTisVg4YFTHug1U9c3C4ZRsDHxY3jnvHd46NuH+Cz/M17c/iIA8aHx3RqkM+4XcOpi3GGJWJctA1M4eFOBQ2fwBN4p4+HkX3uW1RZDwRHBe9FWT655zgrPDTyj77FDoHIPNDkO76/fKZ4UlxHzIDS66+0Sohv0tW99JVgXwk++L/meT/d8ioLCLWNv8V8erOiRhkQNIS4kjqFRQ3lk6iMkmXvnxffBMAoWbgjnr6f9lSkpU3hs02NkxWZxTeY1vj9Q/lew9pGjgvRfwqm3QWSaZ5k/Z4sMT4IR53tuAK5GKDk0+l7wHRz4HmoLoPxnz/r4EZ4Ul6yLIbKf/9olhB/0pW99JVgXwg+cTU4e2vAQAJcOvZTM2ExUVWVT6SYmJEyQwL2P2luzl/7h/dEoGkL1obw460ViQ2I7VTu9JwqGUTBFUTh/0LmcFzkSxRAKh6rt+ERHgvRA0BkhdYLnxk2eZbVFnhH3yH6eaixCiKDXu/9DCBEgr/70Kntq9hBtiuaWsbegqirXrryW70u+57kzn+PUFN9MZiF6jrd3vc3D3z3MbeNu45cjfwlw3JKCvU1ARsFcjVD0A+z/FvZvgP0bUOzVnnX6UE8JwuiBED3Ycz/m0E9LUsdyyAMQpLvdqncfesKTPTchRI8hwboQPlZUX8QLP74AwO8m/I4IYwQAI6JH8H3J9/zjh38wJXmKjK73If/56T88+v2jAGyr2IaqqvL++0NDlSflozk4L9wCTY2tt9GZPLXKnbbDF2Me7USB/L6vAzKSnltW15JOZHc1YdJpGRxnZnZm77yoTgjhIcG6ED5W56gj1ZJKpDGy1aQxCzMX8vbut9lxcAdrD6xler/px96J6DVe/+n1lkD9V1m/kusXfEVVPXXA9284HJyX72y7XVg89DsZ+k32/EzM8iyv3g8H8zwXWlYe+nkwz7P8eIG8zuSZ0AgOB+lTF0NEqv9eK55A/eWv86m0OkiKMBFqCMHmcJFdVENRTQMLpwyQgF2IXkqCdSF8bGj0UN4+921qGmtaBWUxITHMHzaff2X/iyVbl3B62ulolGNWXRY+5HarFFQ1UGSFgqoG+sfquiVf+o2db/DX7/8K9IJA3e2GmgMYnTUBOn6TJ3jev/FwcF5X1Ha7mIzWwXn0oPZTWmIGe25Ha3IeEcgfEcRX7vEsd9m7NUgHz/m7IruUSquDjHhzyzlkMekxG3XklNWzckcpg2LNvbYahhB9mQTrQviBXqNvmS7+SFePvJo3d73JrqpdrN6/mpn9ZwagdX1Lc+pATmkt+QUadq3OJSMh3O+pA2/sfINHvnsEgOuyrus5gXpDFVTkwsFcOJgDFTktgaveZWcOoB547FDd7kO3xCzPxYy+1FgPhZsOB+cFm8BR13objQ6SxrQOzsO8vHBUqz92IO9yeGqZmyIhLMa743RCYXUDeeWe0pdHn0OKopAUYSK3rJ7C6oY+Ux1DiL5EgnUhfOT5H59Ho2i4euTVGLSGdreJNEVy1fCreGHbCzy79VnOSDsDrUbbzS3tO45MHUi0GLCFQFSovltTB67NvJbfjP1NcAXqrkaoyj8UiOd4AvPmAN1WccynqRo9uF0oNfuhZj9kv+dZoTVA0ujDwXvqSZ4R58685tpiOLCh5UJQSraD2tR6G2O4Z9/9J3uC8+Rx3Ttpj87QfhDvZ1aHC7uriVBD+5NHhRi0lNbasTpc3dwyIUR3kGBdCB/YU72HF7a9gMvtYnj0cKamTj3mtr8c+UuW/rwUgPKG8j5VEaQ7HZ06oKpuNAqYTToyQgx+Tx24cviVjIwZyei40YEN1FXVE5TnrYG966BsJ1TvA9V97OdYkiE2HWLSPWklsRkQk44rLImV//uQ2Vlx6Ip/8Ix2F3wHtoOeSXgKvj+8D3PiobKBh4L35DFgCPOsc7s9tb6PDM6r97VtR0SaZ7Q8bRLutJMp1A/A6lJ7/QQoRwsz6DDptNgcLiymthMpNTiaMOq0hBnkX7oQvZH8ZgvhJVVVeWjjQ7jcLqalTjtuoA6eCVpen/s6AyIGSM66Hx2dOqCqh9d1NnWgo+XylucvZ3LS5JYKQGPix/jyJXVcQxXsWQd5qyHvC0/qxtEMZk8wfigQb7kfPdgzHX17nE5c2hDUAadBxgzPMlWFqr2HAvdDAXvJdqgvgZ8/9dwAFK2nrndorCe9xX5U7ruigYSRnhHztEmeIP1QPvjhKih5fbIKSkpkCIPjzGQX1WA26lp9+FNVleIaO1kpEaREtj/yLoTo2SRYF8JLn+75lO9LvsekNfH7Sb/v0HMGRQ7yc6uEr1IHOlou7+1db/PghgcZHj2cV+a8Qqi+G9MzmlxQuPlQcL7Gc//IkXOt0ZM6MvgMT+pIbAaYEzqXpnIsinKozOEgGHWpZ5mzAYp/9ATuB77z/Kwr9ixrpg/1jLw3B+epJ4EpvM3upQqKp0b97MwEimoayCnzfAANMWhpcDRRXGMnOszArJEJfeabBiH6GgnWhfBCraOWxzc9DsANo28gxZzSqec3uBr4OPdjLhxyIXpN26+3Rdf5InWgo4Fic6AOMDFxIiG6bhjhrNrnCczzVsOe9dB41Eh13DBPcD54BvQ/pXtzu/Uhhy76PPnwsppCT9Buq/B8YEjM8lzMeRxSBeWw9HgLC6cMaPngWFprx6jTkpUSwayRHf+GwetJlYQQ3U6CdSG88PSWp6m0VzIwYiALRizo1HNVVeWqZVexu2o3eq2eCzMu9FMr+6ajUweO1JHUgY4Gilsql/PgRk+gvmDEAm6fcLt/ctSbnJC7+vDo+cHc1utDomDQNE9wPnh6t5QU7JSIFM+tE6QKSmvp8RYGTTN3OdiWSZWE6JkkWBeiiw42HOSj3I8A+MOkP6A/wSjh0RRF4bzB5/H4psd54ccXOHfQuZ3ehzi2o1MHEiwG3CrU2V2U1jlOmDrQkUBxbdHH7Nz/MgC/HPFL/wTqrkbY+gZ8+XdPBZaWRmghbeKh4PwMzwWcvayykFRBaUujUbr0wUTSiYTouSRYF6KLYkJiePe8d1l7YC2TkiZ1aR+XDr2UV3a8QpG1iA9yP+DSoZf6tpF93JGpAzmltZQ1QKjN2aHUgRMFikVNX7HT5QnUfzHiF/xuwu98G6g77fDDf+CrJ6G2wLMsLB6Gn+MJ0AdOBVOE744XhKQKim9IOpEQPZv8hRPCC/3D+7NgZOfSX44UogvhuqzreOS7R/jntn9yfvr5GLU+nlymj2tOHdhXUcfyzw8wZ0Y6/WMtJwxKThQoWhiMkSjmDpzNHRPu8F2g7myAza/C1096LsoEsCTBqbd5Zs3U952KH1IFxTcknUiInk3qxgnRSRUNFWwr3+az/V085GISQhMotZXy7u53fbZfcZhGo5AaFUJyGKRGdSzHtzlQLK6xox5Z9xFPoFhfH8XlKU9w35S7fROoO6zwzT/gyVGw/C5PoB6eAmc9Dr/ZCpNu6FOBOhxOZYoO89TFr7M7cbnd1Nmd5JTVSxWUDjr8LVH743MhBi2NrqY+lU4kRE8iwboQnfS3TX/jqmVX8Ur2Kz7Zn1Fr5PpR1wPw0vaXsLvsPtmv8E57geLP9avJqf2+JVCcN2ooWq2Xf0Yb6z2pLk+OgpV/AGsZRPSDc56E3/wAE38FepMvXlKP1JzKlJkcQbXNSX6FlepDqUySZ90xR35L1B5JJxIiuMlvphCd8H3J93y651MUFCYkTvDZfi9Iv4B/Z/+bETEjqHfWY9L13eAsmDQHisu3l7C+5FN2ul5GQcsliY9zxdiJ3gWK9lr4/kXPaHpDpWdZ1ACY+jsYffkJyxr2Jd5WQenrJJ1IiJ5NgnUhOsjZ5OShDQ8BngtDM2MzfbZvvVbPe+e9R5g+zGf7FL7RoOSz2fl3drq+B+CcARdwz6nTuz6i3lAN3/0Tvl0C9mrPsujBcNrvIOsSCdKPoatVUIRMqiRETyfBuhAd9OpPr7KnZg/RpmhuGXuLz/cvgXpwya/J5+kfnmbVvlUAGDQGrsm6hptG39S1HPWGKtjwHGx4/vAERrFD4LQ7YOSFoJU/x8J/fDWpUm8gE0MJ6Fnngfx3EKIDCusLeeHHFwD43YTfEWH0X8m8ovoiXtnxCr8Z+xvMBrPfjiOOrcHVwPxl86lz1KHgqYe/aMwiksxJnd+ZvRY2Pg/fPAONtZ5lccPh9DtgxLxeVxtdBC9JJ5KJoYRHTzsPJFgXogMe+e4R7E12JiRM4JxB5/jtOKqqcsuaW9hdtZsYUww3jL7Bb8cSrdmcNkL1njSLEF0Ivxj+C346+BO/GfcbMqIyOr9Dh82Tk/7Vk4dz0uNHwul3wvDzQCPX94vu15fTiWRiKAE98zyQ/xZCnICqqpyRdgZxIXH88eQ/+mcq+UMUReG6rOsAT9pNraPWb8cSHo4mB//56T/Mfm82G4o3tCy/YfQNPDPjmc4H6k67J9XlqdGw6s+eQD0mAy7+N9z4FYycJ4G6EN3s6ImhLCY9Wo2CxaQnI95MpdXByh2luN3qiXfmg7YcqLTxc0ktBypt3XJM4RFM50FnyMi6EMehqiqKonBBxgWcM+gc9N1w8d/sAbP557Z/kludy2s7XuOGTBld9we36uZ/e/7HP374B0XWIgDe3/0+JyedDIBG6WRA3eSEH16H9Y9BbaFnWWR/mHb3oQtH5c+tEIESLBND9bT0i94mWM6DzpL/HkK0Y2vZVp754RnOGngWFw25CKBbAnXwBIk3jbmJxWsX8/rO17ks47JuOW5foaoqXxZ8yVNbnmJX1S4A4kPiuWnMTZyffn7nd+hugm1vw7pHoCrfsyw8xXPh6NirpLqLEEHg8MRQ7ZenDDFoKa21+3ViqJ6YftHbBMN50BUSrAtxhB0Hd/CPH/7BV4VfAVBiLeGCjAs6P8rqpRn9ZjAsehg/V/7Mf3b+h8EM7tbjH63J3YS2l1wIed/G+/hkzycAWPQWrsm6hiuHX0mIrpM1pt1u+OlDWPswVOz2LAuLh6m3w/ir+/RERkIEmyMnhrKY2n6A9vfEUEenXzSP6lpMesxGHTll9azcUcqgWHOfuuC3uwX6POgqSZwUAthdtZtbv7iVyz+9nK8Kv0KraLko4yJemvVStwfqcGh0ffRNAPx313+pd9d3exualVhLOOeDc7ji0ytwup0Ba4evTE6cjEFj4OqRV/PZRZ9xXdZ1nQvUVRV+XgYvTIV3F3oC9ZAoOPN++O1WOPlGCdSFCDLNE0MV19hR1db5yM0TQ6XHm/02MVRn0i+E/wT6POiq4ProIEQA/Gv7v3hqy1OoqGgUDWcPPJsbR99Iv/B+AW3XtLRpTEycSGZMJrqCwPyqOt1O7lh3BwX1BWTFZaHX9LyUjm+KvqHJ3cTJCZ5c9Fn9Z3FS8kkkhiV2bkeqCnlrYM1DULTFs8wYDpNvhpN/DaZwH7dcCOErgZ4YqqemX/Q2gT4PukqCdRHUPs77mFX5q3hmxjMty44ssecL4xPGo6Iye8Bsbhp9E4MiB/ls395QFIWXZr2Ey+ViWeGygLThmR+eYWv5VoBWE0GV2cqINkWj0wTvnxCX28WzW5/lpe0vYTFYeHPum4DnW4t2A3W3G2wVUFsEdSVQd+hn8+OqfDiY49lWH+YZQZ98M4RGd9+LEkJ0WSAnhuqp6Re9UU+cIEzOChHUXtz2IglhCRTXF5NkTsLpdjLt7WnEh8aTFZtFZmwmWbFZDIsehkFrOOH+SqwlvLDtBSIMEdw6/lYAxsSPYdmFy0izpPn51XTekV+X1jpqCdeEd9uFrusL1vNy9ssAPDHtiZb+sTqtXLfyOmJDYnn0tEeJDYntlvZ0Rom1hDvX38kPZT8AMGfAbCJtVcTW/YSyvR6spUcF5MVQXwLuE4xqaY1w0nVw6m1gjuuGVyKE8KVATQzVnH6RXVSD2ahr9be9Of0iKyUi6NIvequeNkGYBOsiaO2t2Ut+bT75tfmEGz0pBvk1+TS4GthXu499tfv4dM+nAOg0OoZFDePCIRdyyZBL2uyr3FbOS9tf4p3d7+B0OzFqjVw98moiTZEAQRmoH6miqYIFKxYwLmEc959yv19rvYMn2P3DV38AYP6w+czsP7NlXU5VDmW2MvbW7OWyTy7jb9P+xpj4MX5tT2esO7CWP3x5DzXOOsyKjnvdkcxZ+yI0/o0pALnHe7YC5niwJHlu4Umt7yeOliBdiB4uEBND9dT0i96sJ00QJsG6CFprD6wFYEryFML0YQBkRGXw5WVfkn0wm+3l29lesZ3simyqGqvIPpjNdPv0lueXWEv489d/Jj40nhX5K7A32QGYkDCBW8be0hKoB726YnTV6zigPcC+un0MiBjANZnX+O1wTe4m7lx/J9WN1YyIGcHtE25vtX5M/Bj+e/Z/ue2L28iryWPh8oXccdIdXDHsCr9/iGhDVT1pKkU/oBZu4fHCVbxGNQAjGht5vKyINNcez6Y6E/W6aMIS09FEpLQfkJsTpB66EMIvemL6hQgOXf6vtH79eh577DE2b95McXExH3zwAfPmzWtZr6oq9957Ly+++CLV1dVMmTKF5557joyMLkzbLfqk5mB9Wtq0VssjTZGcmnIqp6acCnjOtYL6ArIrshkaPbRlu23l2/i2+NuWx6PiRnHL2FuYlDip+4PKrirJRvf6hSyoL0UXEcEj0RE8uflJ+lv6M6P/DL8cUqvRcmHGhRTUFfD4aY+3m140MGIgS89eyr3f3Mvy/OU8/N3D/Fj+I/dOvten1xO0UV8ORT94LvAs+sFzqy8FQAEaYqIg3MJVtfXcZuyHYczZkDwOksfiihrMmuUrOeuss9Doe96FskKInq+npV+I4NDlYN1qtTJ69GiuueYaLrzwwjbrH330UZ5++mleffVVBg4cyJ/+9Cdmz57NTz/9hMkkZc3E8VXaK1subDw99fTjbqsoCmmWtDapLFmxWfzp5D+xt2Yvk5MnMzVlas8J0gH2fglvzkdprMWpCeHKmhrydRreDLdw9xe38cqIXzFi/I1+mXRnXvo85gyYg0l37N/VUH0oj572KKPiRvHEpidYtncZIboQ7jvlvrYbO2xQmQfOBnBYwWk76r7Ns83x7tsOHp4Z9AhORYs+fjgkj+XOxCzODDFxyojLQWc8asOeX3ZSCNHz9aT0CxEcuhysz507l7lz57a7TlVVnnzySf74xz9y/vmeGQFfe+01EhIS+PDDD7n88svbfV5jYyONjY0tj2trawFwOp04A/CPtvmYgTh2b9HVPly7by1u1c3QqKHEGmO79B7EGmO5YNAFLY9drp5TEkvZ+THaj25EaXLQlDqJVVFXc8aYAdyx5V/sP7ieb0JM3LL9Wd746h/Ejb0G99hfQph3F3qWN5SjU3REmaIA0KLtUL9fnnE5QyKG8Pjmx7kh84bWzynZhuaH/6DZ8S5KY51X7QNQUSAmHTV5LPaETB637WZfk5UlZzyPVqNFC5wEOFXaBOfy++w96UPvSR/6hvSj96QPvedtH3b0eYp6dFX4LlAUpVUazJ49exg8eDA//PADY8aMadnu9NNPZ8yYMTz11FPt7ue+++7j/vvvb7N86dKlhIbKp9C+5G3r22xzbmO6cTozQvyT7hGsBpavIqvgdRRUiiLGs3nAr3FrDqeiuB2l/LP+RQo0dmZYbTxZVkGToqcg6mT2xs2kJnRAp4/ZpDbx7/p/U+WuYn7YfFJ1qZ3eh6qqKIqCrqmBlKoNFNR9wZzq/JYRAYc2DKc2DJfGSJPGQJPG2Op+yzKtkSbFSJO29XqnJoS6kFRc2hDKm8p5y/oWJe4SABaGLWSwPrCzvAohhBCdYbPZmD9/PjU1NYSHH3uuDr9cSVVS4vkHmpCQ0Gp5QkJCy7r23H333SxevLjlcW1tLWlpacyaNeu4L8JfnE4nq1atYubMmeglx7VLutqHM5tmsqV8C6nmVFLMKX5sYRBRVTRr/w9twX8AaBp3NXGz/8qMJnebPhxbP4vHNz3KPZFjcW95A23xD/Sv/JL+lV/iTjsZ90nXow49CzpYB/2Zrc+w76d9hOnCmDN9Dv0snZwQSlVRin5A88OrKDs/5DODyt3xsXxgSuCRqAlEjbsWpf+pGBQNJy6weXyf7v2Uf37/TxrcDUQZo3hw8oOcknzKCZ8nv8/ekz70nvShb0g/ek/60Hve9mFzBsmJBFXZA6PRiNFobLNcr9cH9EQK9PF7g872oV6v59S0U/3YoiDT5IRPboOtr3seT/8j2tN+h1ZRWtI5juzDAVED+MfMZz3bTrgOCjbBxufhpw/RHNiA5sAGCE+FidfBuAXHnbjnq8KvePknTz31+6bcx+DoToxQN1TDtrdhy6tQmt2yWBc9iBAFvguBKzRlPBEZxyhD29/tzrA5bfzfxv/jo7yPAJiYOJGHpz5MfGh8p/Yjv8/ekz70nvShb0g/ek/60Htd7cOOPscvwXpiomd2wNLSUpKSklqWl5aWtkqLEULgucjynashZyUoGjjnSRi/oOPPVxQ+sBfA6HO4YNaDsOnfsOllqC2Az++DtY9A1iXQf8qhMoXJnp9GC6XWUu758h4ALht6GXMGzDnx8VQV9m/wBOg7PgRXg2e5zgQj5sH4BczqN5nBNXu49Ytbya/NZ8HyBVyXdR1xIXFMSJzAoAjPLLEH6g6wat8q3Kobt+qmSW1CVdWWn6ennc7ouNEA3P3l3aw5sAaNouHG0Tdyfdb1aDXajveTEEII0QP5JVgfOHAgiYmJrF69uiU4r62tZePGjfz617/2xyFFL6GqKlcvv5qRsSO5Puv6nlMLvausB2HpJVC42RPsXvwyDDurU7v4tuhb/vzNn9EpOlJn/ZOTzvgjTP0d7HgfNjwHJdvgh/94bkdwGSzcmRBNlU5lmCaMO+qd8N2LEJ58qP54MoTFQXNAbKuEH/8Lm1+Fil2HdxQ/0vPhYtSlEBLVsnhw5GD+e/Z/+dPXf+Lz/Z/z/I/PA/DAKQ+0BOv5Nfn8ffPfj/naYkJiWoL1m8bcxO6q3Tww5QFOSjypU30khBBC9FRdDtbr6+vJzT08FeDevXvZunUr0dHR9OvXj1tvvZWHHnqIjIyMltKNycnJrWqxC3G0nZU72VK2hZ2VO/ntuN8Gujm43ar/6uFW7YPXL4SDuZ4g94q3oN+kTu/m5KSTmTtgLp/lf8atX9zKG2e9wYCIATBmPoy+wjMKvu1NqMqH2mKoK4bGWl4LgS06lTC3m8cP5GDM29l254oWLImeWT1Ld0CTw7NcHwqZF8K4qyF1AhyjJKbZYOaJaU/wzu53+LrwazSKhiTz4W/bEsISOG/weWgVLRpF0+qmVbQMjTpcN39o9FA+ueATdB3MwxdCCCF6gy7/19u0aRPTpx+eLbL5wtAFCxbwyiuvcOedd2K1Wrn++uuprq7m1FNPZfny5VJjXRxX80RIpySfglHrXY6zt3LL6lpmmrO7mjDptAyOMzM70wczzZVsh9cv8kzoE5EGV70HcUNP/Lx2KIrCg6c+SKG1kG3l27h5zc28cdYbRBgjPEF0/8me25Ea67j4YC7bt/yN2WED6Z8eeTiQry3y/KwvBbXJU9u8ub550mhPDnzWJWDq2EXfiqJw6dBLuXTopW3WDYkawl9O/UuHX6sE6kIIIfqaLv/nmzZtGser+qgoCg888AAPPPBAVw8h+qBjzVra3XLL6nj563wqrQ6SIkyEGkKwOVxkF9VQVNPAwikDuh6w710Pb14JjbUQP8ITqIcne9Veo9bIU9OfYv7/5rOvdh+3rb2NF858Af2xJkwyWghPHssTSf859kRRTS5PwF53KIiP7A9Jo7xqpxBCCCE6RxPoBgjRrMRaws7KnSgoTE2ZGrB2uN0qK7JLqbQ6yIg3YzHp0WoULCY9GfFmKq0OVu4oxe3uwhQF2e97RtQbaz0XfC78zOtAvVlsSCz/mPEPwvRhfF/yPQ9ueLDNB2qX28Wqfatalh93RletDiJSPGkuw8+VQF0IIYQIAAnWRdBoHlUfHTeamJCYgLWjsLqBvPJ6kiJMbYJZRVFIijCRW1ZPYXVD53a84Xl49xpP3vfw8+Cq9yEk0ncNx5NW8uhpj6JVtCSFJbVZ/9yPz7F47WLu+/Y+nx5XCCGEEP4hCaAiaARLCozV4cLuaiLUENLu+hCDltJaO1aHq2M7VFVYfT98dajqyUm/grl/PVxlxcdOSz2Nj+d9TL/w1hMbfVP4DS9uexGASYmdv5BVCCGEEN1PgnURNAZGDCSnKofpadNPvLEfhRl0mHRabA4XFlPbnO8GRxNGnZYwwwl+fRw2yFkBW16DvDWeZWf8CabefszqKb5yZKDe4GoguyKbu7+6GxWVS4ZcwlmDOlceUgghhBCBIcG6CBp3TbyLO0+6M9DNICUyhMFxZrKLajAbda1SYVRVpbjGTlZKBCmR7Yy8uxyewDz7Xfh5GTitnuWKFs59Csb9optehUdFQwU3r76ZHQd3ADA0amhQ9LEQQgghOkaCdRFUjnvBYzfRaBRmZyZQVNNATpkndz3EoKXB0URxjZ3oMAOzRiYcrrfuboL8LyH7PfjpY7BXH95ZZD/IvAhGXQ7xw7r9tRi1RuwuOwChulAeP/1xTDopnyqEEEL0FBKsi4BrcjexrWIbo2JHBc308enxFhZOGdBSZ7201o5RpyUrJYJZIxNIjzPD/o2eAH3HB2AtO/xkcwKMvNATpB9nwqDuYDFYePbMZ3n+x+c5e9DZnsmShBCii/w6UZwQol0SrIuA+7H8RxYsX8CA8AF8PO/joBhdB0/APmia+fA/Jr2WlMZcND8+BtkfQM3+wxuHRMGI8z0Bev8pfrt4tCuSzck8MEXmOxBCeMevE8UJIY5JgnURcM1VYDJjM9sG6js/he9fgun3QNrEbm+bRqOQphbDz+/A9nfhYM7hlQYzDDsbMi+GQdNAZ+j29gkhRHfw60RxQojjkmBdBNwXB74A4PS001uvUFVY+Ueo2gv5X3nKHU64pvvSSlQVvv0HfH4fuA+VadQaYchsyLoYMmaBvv3yjkII0VscPVFc86CKxaTHbNSRU1bPyh2lDIo1S0qMEH4gwboIqL01e8mvzUen0TEleUrrlQe+8wTqAG4n/G8xFG6Bs/8Gej9fJGmrhA9vgt2feR4PPA3GXAlDzwJTuH+PLYQQQaQzE8WlRYcGqJVC9F4SrIuAWndgHQAnJZyExXDUV6g//tfzc/QVED/cM8K99XUozYbLXofINP80qmATvLPQk5OuNcKch7t3RF8IIYKIzyeKE0J0iibQDRB92zFTYJx22PG+5/7oK2DKb+Gq9yEkGoq3wj9Phz1rfdsYVYVvn4V/z/EE6lED4bpVcNK1EqgLIfqsIyeKa0+HJ4oTQnSJBOsiYKrt1Wwt3wrAtLRprVfu/gzsNRCeCgOmepYNng43rIOk0WA7CP+5AL5+yhNke6uhGt66Clbc7Um5GTEPbljvOZYIKLdb5UCljZ9LajlQacPt9sH7LYTosOaJ4opr7KhH/b1tniguPd7c/kRxQgivycdgETDhxnBem/saP5b9SIo5pfXKH9/0/Bx1KWiO+EwZ2Q+uWQH/ux22vgGr/uzJYz9/CRjNXWtI4RZ452qo3gdaA8z+PzjpOhlNDwJSKk6IwOv0RHFCCJ+SYF0EjEbRMDpuNKPjjhq9ri+HnFWe+6Mvb/tEfYgnOE8ZB5/9Hn76EMp/hsvegNj0jjdAVeG7f8KKP3hG0yP7w6WvQvLYLr8m4TtSKk6I4HHCieLkd1EIv5FgXQSf7HdBbYLkcRA3tP1tFMUz+p2QBW//0hOsvzgdLngBhp114mPYa+DjW+CnjzyPh53j+QAQEumzlyG6TkrFCRF82kwUJzOYCtEtJGddBMSmkk3c9819bCje0HZlcxWYMfNPvKN+kzy55f0mQ2MtvHkFfPF/4HYf+zlFW+GF0z2BukYPcx7xVJeRQD1odKZUnBCi+2g0CmnRoQxLDCctOlQCdSG6gQTrIiBW5K/gvZz3WJG/ovWK0p+g+EdPED3ywo7tzJIAv/wYJt7gebzur/Dfy6ChqvV2quqZDfVfMz312yMO5b+f/GvJTw8yh0vFtf/lX4hBS6OrSUrFCSGE6PUkWBfdTlVV1hasBWB62vTWK5tH1YfMhrCYju9UZ4CzHvWkwehMkLMS/jkNSrI96+218O41ngtTmxww9Gy4cT2kjvf69Qjfk1JxQgghhIf8pxPdblfVLkqsJYToQpiYOPHwCncTbHvbc7+9C0s7YvTlngmU3roKqvI9o+jT7obNr0BlHmh0cOb9MHmRjKYHseZScdlFNZiNulapMM2l4rJSIqRUnBBCiF5PRtZFt2ueCGly0mRMOtPhFXvWQn0JhERBxqyuHyBpNFy/DgafAU4brPqTJ1CPSIOFy+GUmyVQD3LNpeKiwwzklNVTZ3ficrupszvJKauXUnFCCCH6DAnWRbdbe2At0M5ESM211TMvAp3Ru4OERsOV78Kpi0HRwJC5ngtR007ybr+i2zSXistMjqDa5iS/wkq1zUlWSoSUbRRC9GkyWVzfImkwoluVWkv56eBPKChMTZ16eEVjHez8xHN/9BW+OZhGC2feC6fdAYZQ3+xTdCspFRc83G6VgqoGiqxQUNVA/1idvA9CBIBMFtf3SLAuulWJrYQB4QOIMEYQGxJ7eMVPH4OrAWIyIMXHF31KoN6jNZeKE4HTHBzklNaSX6Bh1+pcMhLCJTgQopvJZHF9kwTroluNjhvNJxd8Qr2jvvWK5iowoy+XfHIhgsiRwUGixYAtBKJC9RIcCNHNZLK4vkty1kVAmA3mww+q90P+l577oy4LTIOEEG0cHRyYTTo0CphNOjLizVRaHazcUSr5skJ0A5ksru+SYF10m0p7JY4mR9sV297y/BwwFSLTfHpMuQhHiK6T4ECI4CGTxfVdkgYjus3fN/+dlfkr+f3E33NBxgWehap6uAqMry4sPUQuwhHCO4eDg/br2YcYtJTW2iU4EKIbHDlZnMWkb7NeJovrvWRkXXSLJncT6wvWY3PZSDGnHF5RuBkO5oIuBEac57PjNefZZhfVEBmqZ1CsmchDebYvf51Pblmdz44lRG8lM8kKETyaJ4srrrGjqq2/JW6eLC493iyTxfVCEqyLbpF9MJtKeyUWg4WxCWMPr2i+sHT4uWD0zWj30Xm2FpMerUbBYtJLnq0QnSDBgRDBQyaL67skWBfdYl3hOgCmpkxFrzn09Z2rEbLf89wffbnPjiV5tkL4RtvgwIVbhTq7S4IDIQJAJovrm+S7S9Et1hV4gvVWs5bmrISGKrAkwaBp7T6vKyTPVgjfaQ4OmuuslzVA6KHgYNZIuf5DiO4mk8X1PRKsC7872HSQvXV70Sk6pqRMObxi66EUmFGXemYb9RG5CEcI32oODvZV1LH88wPMmZFO/1iLBAdCBIhMFte3+DUN5r777kNRlFa3YcOG+fOQIgj97PwZgPGJ4wk3hHsWWg9CzgrP/VG+S4EBybMVwh80GoXUqBCSwyA1SkbxhBCiu/h9aHHkyJF8/vnnhw+ok9HMvmaofiiDhg5iUOSgwwuz3wO3C5JGQ8IInx6vOc+2qKaBnDJP7nqIQUuDo4niGrvk2QrRR7ndqqQOCCF6HL9HzjqdjsTExA5t29jYSGNjY8vj2tpaAJxOJ06n0y/tO57mYwbi2L2F0+kkVhvLzCEz0ev1LX2p3boUDdCUeSluP/Rv/ygTV01MZdXOMvaUW2l0uTHqNIxINHPm8Hj6R5l6zPsq56FvSD96ryf3YW5Zfcvfg+Z5FwbFhTFzeDzp8eYT78BHenIfBhPpR+9JH3rP2z7s6PMU9eg8AR+67777eOyxx4iIiMBkMjF58mQefvhh+vXrd8zt77///jbLly5dSmio5Gb1FmZ7ITN23o0bDSsyn8ahD/fbsdwqVDVCYxMYtRBlBBlIE6JvKbHBuhIFq1MhygAGLTiaoMoBYXqV0xNVEuVfjBCim9lsNubPn09NTQ3h4ceOhfwarH/22WfU19czdOhQiouLuf/++yksLCQ7OxuLpW0FgfZG1tPS0qioqDjui/AXp9PJqlWrmDnTMyrc07jdKkU1dqyNLsKMOpIjTN3yla9bdXOw4SAF9QW88fMbxFTGcOOsG4kKjQJA88VDaL95Enf6LJouW+r39vR0Pf08DBbSj97riX3odqu88OVedhTVkhEf1qqcq6qq5JRZyUwO5/qpA7vl72NP7MNgJP3oPelD73nbh7W1tcTGxp4wWPdrGszcuXNb7o8aNYpJkybRv39/3n77ba699to22xuNRoxGY5vler0+oCdSoI/fFblldazILiWvvL7lK9/BcWZmZ/qm1JrNacOkM6FRPNcof5j7Iav2raKgroDC+kIamxpbbX+27WziI+LB7YbsdwDQjL0STQ/r10DqiedhMJJ+9F5P6sMDlTbyDzaQEhWKVtv2X15KVCh7DzZQZnV1a3WNntSHwUz60XvSh97rah929DnderVnZGQkQ4YMITc3tzsP2+fkltXx8tf5VFodJEWYCDWEYHO4yC6qoaimoVMTJ+RV57GtfBsF9QUU1BW0/Ky0V7Lq4lUkhnmuR8ivyWd9wfqW52kVLYlhiaSEpWCpsZAVk+VZkb8eagvBFAFD5vj8tQshxJFk3gUhRE/XrcF6fX09eXl5/OIXv+jOw/YpbrfKiuxSKq0OMuLNLV/5Wkx6zEYdOWX1rNxRyqBY8wm/8l22Zxm///L3qLSfKVVYX9gSrM/oN4NUSyop5hRSLakkhiWi13guKF22bNnhr55/fNPzc+SFoDf55kULIcQxyLwLQoiezq9/nX73u99x7rnn0r9/f4qKirj33nvRarVcccUV/jxsn1ZY3UBeuadc4ZG5mQCKopAUYSK3rJ7C6oYTfuWrUTRoNVpGxoxkaNRQUi2pnps5lRRLyuGa6UBWXBZZcVnHb1xjPfz0sef+aDkHhBD+1zzvQnZRDWajrk3OenGNnayUCJl3QQgRtPwarBcUFHDFFVdw8OBB4uLiOPXUU9mwYQNxcXH+PGyf5suvfOcMnMOAiAEMiRrSkpvulZ8/BacVogZC2kTv9yeEECcg8y4IIXo6vwbrb775pj93L9rh7Ve+e2v2EqILITEsEbdbJYx+7C6t980EIj/+1/Nz9BWgyD9GIUT3SI+3sHDKgJaL7ktr7Rh1WrJSIpg10jcX3QshhL9Ikl4v481XviXWEq5fdT0KCn8c/yTb9xp8V02mtgj2rPPcH31ZV1+eEEJ0SXq8hUHTzDKDqRCix5FgvZfp6le+1fZqblh1AyXWElLC+vHxliqsDSavq8m0tCv7XUCF/lMgaoDvXrAQQnSQRqN0a3lGIYTwBR8kIotg0/yVb2ZyBNU2J/kVVqptTrJSItoNtG1OG4vWLGJPzR7iQ+OZFv4HrA0mMuLNWEx6tBoFi0lPRryZSquDlTtKcbs7MZeWqqLZfiglavTlPnylQgghhBC9m4ys91Id/crX6XZy+7rb2Va+jXBDOPdPfIr3N7hIitB7XU2mWWTDXpSK3aAzwYjzffYahRBCCCF6OwnWe7ETfeXrVt38+es/81XhV5i0JpbMWILJ3Q+7K8enE4ikVX7tuTPsbM9kSEIIIYQQokMkWO/D6hx1/Fz5MzpFxxPTnmBM/BgOVNoOV5Mx6kip3YLJVUu9IZ56YwKlTebOTSDS5CClaoPnvtRWF0IIIYToFAnW+7AIYwSvzHmFH8t/ZGrqVOBwNZm8A4VcVvsUQw+ubvWcJrTYjHGY3+8PEckQngLhyYduh+6bE0DrKRup5K3G6KpDDYtHGTS921+jEEIIIURPJsF6H1RYX0iKOQXwBOynpZ7Wsk6jUTg/Zj9h395IlLOUJrSUmocR1liOxVmBliYsjSVQUAIFxzqC4gnYw5PR2g4C4M68CK1WTjchhBBCiM6Q6KmPWbN/DbevvZ3fnfQ7rhx+ZeuVTS748nFS1/0VVDc1plReTvwjOfohGHVaMuJMzBmgYaChFmoLPbXTW3423y8GtxPqS6C+hOZLVN1Zl6Pt9lcrhBBCCNGzSbDeh2wq2cSd6+/EpbrYVbkLVVUPV3ypPgDv/wr2f+t5POpyLHMf46IG3TGqyUxo/yBuN9gqWoL4psr9fJ9byviEkX5/fUIIIYQQvY0E633Erspd/GbNb2hsamRa2jT+PPnPhwP1HR/CJ78Bew0YLHDOEzDqUjRAWvtFYY5NowFzvOeWPBa300lp+TIfvxohhBBCiL5BgvU+4EDdAW78/EbqnHWMix/HY6c9hk6jA4cVlt8NW171bJgyHi56CaIH+eS4brdKQVUDRVYoqGqgf6xOpvbug9xuVaZ4F0IIIbpIgvVerqKhghtX3UhFQwUZURk8M+MZTDoTlGyHd6+Bit2AAqfeBtPvaani4q3csjpWZJeSU1pLfoGGXatzyUgIZ3ZmQpsZVEXv1Xwe5JXXY3c1YdJpGRxnlvNACCGE6CAJ1nu5Ffkr2F+3nxRzCi+c+QLhegtseA5W/RmaHGBJggtegEGn++yYuWV1vPx1PpVWB4kWA7YQiArVk11UQ1FNAwunDJBArQ848jxIijARagjB5nDJeSCEEEJ0ggTrvdyVw69EQWFKyhTi3MDSSyFnpWfl0LPgvH9AWIzPjud2q6zILqXS6iAj3oyqutEoYDbpyAgxkFNWz8odpQyKNUsqRC929HnQfH2ExaTHbNTJeSCEEEJ0kCbQDRD+N3/4fPqX58HzUzyButYIZz0Oly/1aaAOUFjdQF55PUkRpsMXsB6iKApJESZyy+oprG7w6XFFcJHzQAghhPANGVnvpWodtWjQYNYYYM0D8M0znhVxw+Hif4GfSilaHS7sriZCDe2XkQkxaCmttWN1uPxyfBEc5DwQQgghfEOC9V7qnV3vsGTrEq5zaLnpwG7PwgnXwuy/gL6z9Rg7Lsygw6TTYnO4sJjaXqza4GjCqNMSZpBTrzeT80AIIYTwDUmD6aU+3/c5TreT2OoiCImCy97w1E/3Y6AOkBIZwuA4M8U1dlRVbbVOVVWKa+ykx5tJifRvO0RgyXkghBBC+IYE671QcX0x2QezUVSVM6w2OP9ZGH5Otxxbo1GYnZlAdJjnYtI6uwu3CnV2Fzll9USHGZg1MkEuKuzl2p4HTlxuN3V2p5wHQgghRCdIsN4Lrd6/GoBx9kZiDeGQfma3Hj893sLCKQPITI6g2uakrAGqbU6yUiKkXF8fcvR5kF9hlfNACCGE6CRJGO2FVu1bBcCZtgYYcQHoDN3ehvR4C4OmmdlXUcfyzw8wZ0Y6/WMtMpLaxzSfBzKDqRBCCNE1Eqz3MhUNFfxQ9gMAZ1ptkHlxwNqi0SikRoWQHAapURKg9VUajUJadGigmyGEEEL0SJIG08us2b8GFZUseyOJIXEw4NRAN0kIIYQQQnSRjKz3Mqenno7D8BoxZZshcwFotIFukhBCCCGE6CIJ1nuZBL2Fq/ZsAacNsgKXAiOEEEIIIbwnaTC9ze7PwGmFqAGQMj7QrRFCCCGEEF6QkfVe5LkfnyNh+0ecqVEIz7wIFLmgUwghhBCiJ5NgvZeod9Tz4rYXcbqdZGl1hAewCowQQgghhPANSYPpJb4s/BKn28kAh5P0qHRIGBHoJgkhhBBCCC9JsN5LHJ4IyYYio+pCCCGEEL2CpMH0Ag2uBr4q+BKAM60NkHlRgFskgonbrcoMokIIIUQPJcF6L/BN0Tc0NNlJdroYEZcF0QMD3SQRJHLL6liRXUpeeT12VxMmnZbBcWZmZyaQHm8JdPOEEEIIcQISrPcCn+/7HIAZNhvKxEsC3BoRLHLL6nj563wqrQ6SIkyEGkKwOVxkF9VQVNPAwikDJGAXQgghgly35KwvWbKEAQMGYDKZmDRpEt999113HLbPsNkq0KgqM212GHlBoJsjgoDbrbIiu5RKq4OMeDMWkx6tRsFi0pMRb6bS6mDljlLcbjXQTRVCCCHEcfg9WH/rrbdYvHgx9957L1u2bGH06NHMnj2bsrIyfx+6z3gqdDhr9hcyOukksCQGujkiCBRWN5BXXk9ShAnlqHr7iqKQFGEit6yewuqGALVQCCGEEB3h9zSYJ554gl/96lcsXLgQgOeff57//e9//Pvf/+b3v/99q20bGxtpbGxseVxbWwuA0+nE6XT6u6ltNB8zEMfuDN32d4lxu3ENv5CmIGtrT+nDYNaVPqyx2rE5nCSGG3C7m9qsN+kUGhwuaqx2Ei16n7U1mMm56D3pQ+9JH/qG9KP3pA+9520fdvR5iqqqfvse3OFwEBoayrvvvsu8efNali9YsIDq6mo++uijVtvfd9993H///W32s3TpUkJDQ/3VzB6rSW1C07CHebsexK1oWZ75D5y6sEA3SwSBg3ZYdkCDWQemdj6SN7jA6oKz0tzEmLq/fUIIIURfZ7PZmD9/PjU1NYSHhx9zO7+OrFdUVNDU1ERCQkKr5QkJCfz8889ttr/77rtZvHhxy+Pa2lrS0tKYNWvWcV+EvzidTlatWsXMmTPR64Nv9PH70u/59ep7WRsfyxMR45l5XvBdXBrsfdgTdKUP3W6V+i/3sqOolvT4sFapMKqqklNmZUJyOFdOHdhnyjjKueg96UPvSR/6hvSj96QPvedtHzZnkJxIUFWDMRqNGI3GNsv1en1AT6RAH/9Yvij4AjdgcbvRjLoUTRC2sVmw9mFP0tk+PGtUMqV1DvIqGkiKMBFi0NLgaKK4xk6sxcTcUckYjQY/tjg4ybnoPelD70kf+ob0o/ekD73X1T7s6HP8eoFpbGwsWq2W0tLSVstLS0tJTJQLIb3hVt2s3rscgJmNTTB0boBbJIJNeryFhVMGkJkcQbXNSX6FlWqbk6yUCCnbKIQQQvQQfh1ZNxgMjB8/ntWrV7fkrLvdblavXs3NN9/sz0P3eCeadXJb+TbKHdWEud2c3O8MMEiuumgrPd7CoGlmmcFUCCGE6KH8ngazePFiFixYwIQJE5g4cSJPPvkkVqu1pTqMaKsjs05+vm8VAKfZGjBMvjSQzRVBTqNRSIuWC7SFEEKInsjvwfpll11GeXk5f/7znykpKWHMmDEsX768zUWnwqMjs04OjjPzed7/AJjpBNJnBLbRQgghhBDCL7rlAtObb75Z0l464OhZJ5sreFhMesxGHTll9azcUcrpmfspbDyIye1myoDZoGt7Ua4QQgghhOj5gqoaTF/X0Vknz3DG8kB1AwfdjYSeflmAWiuEEEIIIfxNgvUgYnW4sLuaCDWEtLs+xKCltNZO2IHvuKCqHMwJMGBqN7dSCCGEEEJ0F7+WbhSdE2bQYdJpsTlc7a5vcDRh1GmJ3vOxZ8HIC0Cj7cYWiu7mdqsUVDVQZIWCqgbcbr9NOCyEEEKIICQj60EkJTKEwXFmsotqMBt1bWadLK6xExK+kXf3rme2Vkti5sUBbK3wt+aqQDmlteQXaNi1OpeMhPBWVYGEEEII0btJsB5ENBqF2ZkJFNU0kFNW32bWyegwAzus77EqMoxwfRgXpE4IdJOFnxxZFSjRYsAWAlGh+lZVgSRgF0IIIXo/SYMJMsebdXLuWD15jjK0qsr09PNAkYlteqOjqwKZTTo0CphNOjLizVRaHazcUSopMUIIIUQfICPrQehYs06+9uPzAEywNxI5+soAt1L4y9FVgdQjYvIjqwIVVjfIZEdCCCFELyfBepBqb9bJVTkfAnCmJgISRgSgVaI7dLQqkPUYFyILIYQQ3cFut1NeXh7oZgSM2+0mLS2NoqIiNJr2k1Xi4uIwmUxeHUeC9R6ixFrCtoYiFFVlRvp5gW6O8KMjqwJZTPo265urAoUZ5NdXCCFEYNjtdsrKykhJSUGr7ZuV6dxuNxEREYSHh7cbrDc1NVFYWEh8fLxXAbvkrPcQqw+Nqo9pbCRuzC8C2xjhV81VgYpr7Khq67z05qpA6fFmUiLbH3kXQggh/K28vLxPB+ododVqSUlJ8frbBwnWe4iqgu8wuFXO1MVC9MBAN0f4UXNVoOgwAzll9dTZXbhVqLO7yCmrJzrMwKyRCWg0coGxEEKIwJFA/cR80UcSrPcQN5ccYP3+Ai4cdnmgmyK6wdFVgcoaaKkKJGUbhRBCiL5Dkl57gqp9UPAdYYoGRl0W6NaIbtJcFWhfRR3LPz/AnBnp9I+1yIi6EEII0YfIyHoPULH1dc+dAaeCJTGwjRHdSqNRSI0KITkMUqNCJFAXQggh+hgJ1oNcTWMNM/e9ySXJidQPPzfQzRFCCCGE8Bm3W+VApY2fS2o5UGmTCf/aIWkwQW7dT2/iUsClKJizLgl0c4QQQgghfCK3rI4V2aXklddjdzVh0mkZHGdmdmaCXJt1BAnWg9znOR8AcKYpGUKiAtwaIYQQQgjv5ZbV8fLX+VRaHSRFmAg1hGBzuMguqqGopkGKKRxB0mCCmM1h5RtbIQBnDrkowK0RQgghhPCe262yIruUSquDjHgzFpMerUbBYtKTEW+m0upg5Y5Sn6fE5OfnoyhKm9u0adPYt28f5557LlFRUYSFhTFy5EiWLVvm0+N3lYysB7H12a/RqEA/ZxNDxiwIdHOEEEIIIbxWWN1AXnk9SREmFKV14QRFUUiKMJFbVk9hdQNp0aE+O25aWhrFxcUtj0tKSjjzzDM57bTTWLRoEQ6Hg/Xr1xMWFsZPP/2E2Wz22bG9IcF6EPt894cAzAhNQTEGxwkjhBBCCOENq8OF3dVEqKH9mbhDDFpKa+1YHS6fHler1ZKY6KmqZ7fbmTdvHpMnT+a+++5jzJgxXHTRRWRlZQEwaNAgnx7bG5IGE6RsjXWss3tSYGYPkQtLhRBCCNE7hBl0mHRabMcIxhscTRh1WsIM/htTvuaaa6irq2Pp0qVoNBp+85vf8NBDDzFlyhTuvfdetm3b5rdjd5YE60FKf+A7Himr4HKrgxGjJQVGCCGEEL1DSmQIg+PMFNfYUdXWeemqqlJcYyc93kxKZPsj79566KGHWLFiBR9//DEWi+ci1uuuu449e/bwi1/8gu3btzNhwgSeeeYZvxy/syRYD1L6HR8ww9bAH9LmoOiNgW6OEEIIIYRPaDQKszMTiA4zkFNWT53dicvtps7uJKesnugwA7NGJvhlIsD33nuPBx54gLfffpvBgwe3WpeWlsaNN97I+++/z+23386LL77o8+N3heSsByNXI/z0see+1FYXQgghRC+THm9h4ZQBLXXWS2vtGHVaslIimDXSP3XWs7Oz+eUvf8ldd93FyJEjKSkpAcBgMPDAAw8wd+5chgwZQlVVFV988QXDhw/3eRu6QoL1Y3C7VQqqGiiyQkFVA/1jdd021fuKjU+QGwLnmpLp1++UbjmmEEIIIUR3So+3MGiamcLqBqwOF2EGHSmRIX6LtzZt2oTNZuOhhx7ioYceall++umnk5WVxaJFiygoKCA8PJw5c+bw97//3S/t6CwJ1tvRPKNWTmkt+QUadq3OJSMhvNtm1Fq652O2REVgtoxkgUYylYQQQgjRO2k0ik/LMx7P1VdfzdVXX90tx/IlCdaPcuSMWokWA7YQiArVd9uMWiWVOWxx16OoKrPHXu+34wghhBBCiOAnw7ZHOHpGrQRNNSlNhZhNOr/OqHWkzzZ5rjwe36QlccB0vx1HCCGEEEIEPwnWj3DkjFpDK1axYMs8MppeAtrOqOUvnxV/A8DchImgdE+OvBBCCCGECE4SrB/h8IxaOvZbhnFOagIPxzbirl0HeGbUanQ1+XxGrWZ7ir5nJ43oVJVZExb55RhCCCGEEKLnkGD9CEfOqGU39SNdjQRgX81SwP8zai3b8hwAU1QjkYlj/HIMIYQQQgjRc0iwfoSjZ9QabLkYgG90lbjt+X6fUUsp24Glyc3clNP9sn8hhBBCCNGzSLB+hKNn1LIaZjCkEZyKwoGiJX6dUYvKPSza/zNfFBQxc+Jtvt+/EEIIIYTocSRYP0rzjFqZyRHU2JtItI4FYKs+j6smxvmvbOP29wAwDjgdQ2Saf44hhBBCCCF6FL8F6wMGDEBRlFa3Rx55xF+H86n0eAu/njaY385IZ2Tc2cQ1qRzUKuTm/MMvx2tqcrFjx5uoAKMu9csxhBBCCCFEz+PXkfUHHniA4uLiltstt9ziz8P5lEajkBoVQorFxKXRYwDYkbcCVN/XWN+08x0uD3NwVXIi6tCzfb5/IYQQQgjRM/l1BlOLxUJiYmKHt29sbKSxsbHlcW1tLQBOpxOn0+nz9p1I8zHPn3g3Z7x2JkPsNlz536KmnuTT4/zvp9cByAhJwqULhQC8Vn9p7sNAvH+9hfShb0g/ek/60HvSh74h/eg9b/vQ7Xbjdrt92aRusXDhQl577bU2y3ft2sVf/vIXqqur+eCDD9p97o8//sif//xnNm7cSG1tLYmJiYwbN44lS5aQkJBwzGO63e52+7mjfa+oqh+GivGkwdjtdpxOJ/369WP+/Pncdttt6HTH/nxw3333cf/997dZvnTpUkJDQ/3RzA4bs+8l+leupzByIpsG3uyz/brcDv5WfT91GoU7mEJE5Fyf7VsIIYQQwh/S0tIYNGhQoJvRaTfddBNlZWUsWbKk1fLY2FhuueUWampqeOONN9o8r6KigkmTJjF79mxuvPFGIiIi2L9/P5999hk33HAD/fv3P+Yx9+zZw4EDB9ost9lszJ8/n5qaGsLDw4/5fL+NrP/mN79h3LhxREdH880333D33XdTXFzME088cczn3H333SxevLjlcW1tLWlpacyaNeu4L8JfnE4nq1atYubMmegr+8NLp6Ov/4HJJw0gKm6ET46xdstz1NUqxDe5ufSyR9Aawnyy32DRqg/1+kA3p0eSPvQN6UfvSR96T/rQN6QfvedtHxYVFbWOzVQVnDYftrCD9KGdmvFdr9cTFhZGRkZGu+t0Ol27MeeaNWuora3llVdeaRl4zszMZOrUqVgsFpTjtCEmJoasrKw2y5szSE6kU8H673//e/76178ed5udO3cybNiwVkH3qFGjMBgM3HDDDTz88MMYjcZ2n2s0Gttdp9frA/rLqNfr0aeO4eUBo3iaKn757QPcdtF7Ptn3yj0fATAnNA1TWKRP9hmMAv0e9gbSh74h/eg96UPvSR/6hvSj97rahxqNBo3miEsfHVZ4JNWHLeuge4qgEwOdzUVPWrW9A+uSk5NxuVx89NFHXHzxxSiK0pIGdKznNNNoNO32cUf7vVMXmN5+++3s3LnzuLdjfSUyadIkXC4X+fn5nTlkUOk/5FxcisK7tbtosFV6vT9rQxVrG0sBOGv4lV7vTwghhBBCHN+nn36K2WxuuV1yySUnfM7JJ5/MPffcw/z584mNjWXu3Lk8/vjjlJWV+b29nRpZj4uLIy4urksH2rp1KxqNhvj4+C49PxicPvFWUn/+DwVahU++epBLZ/3dq/2t2/wcdkVhgEtlROYVPmqlEEIIIUQ304d6RrkDcdxOmj59Os8991zL47Cwjo3M/+Uvf2Hx4sWsWbOGjRs38sILL/B///d/rFu3jtGjR3e6HR3ll5z1b7/9lo0bNzJ9+nQsFgvffvstt912G1dddRVRUVH+OGS30OoMzE88hUfLv2FpwWoucbtRjvO1x4nMLtpNVHEp9mHnoGj9WphHCCGEEMJ/FKVT6SiBFBYWRnp6epeeGxMTwyWXXMIll1zCQw89xNixY/nb3/7WboUZX/FLnXWj0cibb77J6aefzsiRI/nLX/7Cbbfdxj//+U9/HK5bzTv1z4S6VfK0Kt9ueb7rO2qsQ7t7OZPtjUw/yXfVZYQQQgghhP8ZDAYGDBiA1Wr163H8Mpw7btw4NmzY4I9dB5wlPIULwgbwRsM+Xv/pNU6ZcFPXdvTzMnA1QPRgSB7r20YKIYQQQohOq6mpYevWra2WxcTE8OOPP/Lmm29y+eWXM2TIEFRV5eOPP2bVqlX861//8mubJPeiC+af/HuWrrmRTe46qop/ICqp88H27358ivjoSBYMP5uETpQcEkIIIYQQ/rF27VrGjm0d11177bXcc889hIaGcvvtt3PgwAGMRiMZGRk8/fTT/OIXv/BrmyRY74J+/U7lMV0ak/ZsIPKHpdDJYL24fAcr1DqUcAu/HHa2n1ophBBCCCGO9Morrxx33fHWH53O7Xa7O1wr3Rt+yVnvC2ZPvpNItxu2LgV7Taeeu3zTMwCMV/Ukpp3sj+YJIYQQQoheQIL1rho0DeKGg6Oe6k0vdeqpy0o3AnBW4il+aJgQQgghhOgtJFjvKkWhYNwV/CIpgct3v0KTy9Ghp+3Z/yU/Ky50qsrMCb/xcyOFEEIIIURPJsG6F2JH/4J8g55CLazd2LEJkpb98AIAU5RQIuOG+rN5QgghhBCih5Ng3Qum0GguDh8OwH9y3jnh9qqqsqxyGwBnpc3wa9uEEEIIIUTPJ8G6ly6b8kd0qspmpZGfd3183G0bi37g9Loa0pwupp0kKTBCCCGEEOL4JFj3UmLiGGbqYgB4ffPTx93W9NNH3FVZzf/CxhJqSeqO5gkhhBBCiB5MgnUfuHLMrwFY5iihomJX+xu53ZD9HgDKqEu7q2lCCCGEEKIHk2DdB0ZnXs4otw6novDJN//X7ja5P3/AxsYymgwWGDK7m1sohBBCCCF6IgnWfeTmjMt5rKyCq3Z/C+2UcfzPtn9yXVICfxs4EvQhAWihEEIIIUTfdvXVVzNv3rxWy959911MJhN/+9vfuPrqq1EUpc0tNzc3MA1GgnWfmXzybczRRKCvL4WfPmy1zuGwsqqhEIDpQy4IQOuEEEIIIcTRXnrpJa688kqee+45br/9dgDmzJlDcXFxq9vAgQMD1kYJ1n1FZ4CTrgXAtWEJqtvdsuqrLc9Tp1GIb1IZN2phoFoohBBCCCEOefTRR7nlllt48803WbjwcHxmNBpJTExsddNqtQFrpy5gR+6Nxi/kP1uW8Kq2jMeylzJ21FUALMvzlHScax6EVm8MZAuFEEIIIfzG5rQdc51Wo8WoNXZoW42iwaQzHXfbUH1oF1sJd911F88++yyffvopM2YE99w3Eqz7UlgsuQkZlDpK+M+2Fxg76iqs1jLWOQ6CRmFu5i8D3UIhhBBCCL+ZtHTSMddNTZnKs2c+2/J42tvTaHA1tLvthIQJvDzn5ZbHc96bQ1VjVattti/Y3qU2fvbZZ3z00UesXr2aM844o836Tz/9FLPZ3PJ47ty5vPPOiSe/9BcJ1n3sypMW8/7Xd7LGVUVx8RY27foQu0ZhQBOMGHZhoJsnhBBCCNGnjRo1ioqKCu69914mTpzYKjAHmD59Os8991zL47CwsO5uYisSrPvYkPS5TPrqz2xU7Ly6/kGqbWWggblRI1E0comAEEIIIXqvjfM3HnOdVtM673vtpWuPua1GaR0zLb9ouVftOlJKSgrvvvsu06dPZ86cOXz22WdYLJaW9WFhYaSnp/vseN6S6NEP5qbOA+Bj627+uP9nlhaWoNVcRG5ZXWAbJoQQQgjhR6H60GPejsxXP9G2R+arH2tbb/Tv359169ZRUlLCnDlzqKsL3hhNgnUfyy2rY0vNXJKdKnVaDcvMJmK1A9haN4iXv86XgF0IIYQQIgikpaWxdu1aysrKmD17NrW1tYFuUrskWPcht1tlRXYplQ0qJ+tGo1dVloWFsjthNhnxZiqtDlbuKMXtVgPdVCGEEEKIPi81NZW1a9dSUVERtAG75Kz7UGF1A3nl9SRFmLBobiKx+FdkON3sSpmJoigkRZjILaunsLqBtGjvvr4RQgghhBCd88orr7RZlpKSwu7du7u/MR0kwboPWR0u7K4mQg0hoInjzJj7wG3FakoCIMSgpbTWjtXhCmxDhRBCCCFEjyDBug+FGXSYdFpsDhcWkx7FPKbV+gZHE0adljCDdLsQQgghhDgxyVn3oZTIEAbHmSmusaOqrfPSVVWluMZOeryZlMiQALVQCCGEEEL0JBKs+5BGozA7M4HoMAM5ZfXU2Z243G7q7E5yyuqJDjMwa2QCGo0S6KYKIYQQQogeQIJ1H0uPt7BwygAykyOotjnJr7BSbXOSlRLBwikDSI+3nHgnQgghhBBCIDnrfpEeb2HQNDOF1Q1YHS7CDDpSIkNkRF0IIYQQQnSKBOt+otEoUp5RCCGEEL2S0WikvLyc2NhYFEUGI9ujqioVFRUYjcYTb3wcEqwLIYQQQohOiY+Pp7a2loKCgkA3JWDcbjcHDx4kJiYGjab9zPKIiAjCw8O9Oo4E60IIIYQQotPCw8O9DkR7MqfTydatW8nKykKv1/vtOHKBqRBCCCGEEEFKgnUhhBBCCCGClATrQgghhBBCBCkJ1oUQQgghhAhSQX2BqaqqANTW1gbk+E6nE5vNRm1trV8vHOjNpA+9J33oG9KP3pM+9J70oW9IP3pP+tB73vZhc3zbHO8eS1AH63V1dQCkpaUFuCVCCCGEEEL4Xl1dHREREcdcr6gnCucDyO12U1RUhMViCUjB/draWtLS0jhw4ECfLk3kDelD70kf+ob0o/ekD70nfegb0o/ekz70nrd9qKoqdXV1JCcnH7NOOwT5yLpGoyE1NTXQzejzdUR9QfrQe9KHviH96D3pQ+9JH/qG9KP3pA+9500fHm9EvZlcYCqEEEIIIUSQkmBdCCGEEEKIICXB+nEYjUbuvfdejEZjoJvSY0kfek/60DekH70nfeg96UPfkH70nvSh97qrD4P6AlMhhBBCCCH6MhlZF0IIIYQQIkhJsC6EEEIIIUSQkmBdCCGEEEKIICXBuhBCCCGEEEFKgnUhhBBCCCGClATrx7BkyRIGDBiAyWRi0qRJfPfdd4FuUo9y3333oShKq9uwYcMC3aygtn79es4991ySk5NRFIUPP/yw1XpVVfnzn/9MUlISISEhnHnmmeTk5ASmsUHqRH149dVXtzkv58yZE5jGBqmHH36Yk046CYvFQnx8PPPmzWPXrl2ttrHb7SxatIiYmBjMZjMXXXQRpaWlAWpxcOpIP06bNq3N+XjjjTcGqMXB57nnnmPUqFEts0NOnjyZzz77rGW9nIcndqI+lHOw8x555BEUReHWW29tWebvc1GC9Xa89dZbLF68mHvvvZctW7YwevRoZs+eTVlZWaCb1qOMHDmS4uLilttXX30V6CYFNavVyujRo1myZEm76x999FGefvppnn/+eTZu3EhYWBizZ8/Gbrd3c0uD14n6EGDOnDmtzsv//ve/3djC4Ldu3ToWLVrEhg0bWLVqFU6nk1mzZmG1Wlu2ue222/jkk0945513WLduHUVFRVx44YUBbHXw6Ug/AvzqV79qdT4++uijAWpx8ElNTeWRRx5h8+bNbNq0iTPOOIPzzz+fHTt2AHIedsSJ+hDkHOyM77//nhdeeIFRo0a1Wu73c1EVbUycOFFdtGhRy+OmpiY1OTlZffjhhwPYqp7l3nvvVUePHh3oZvRYgPrBBx+0PHa73WpiYqL62GOPtSyrrq5WjUaj+t///jcALQx+R/ehqqrqggUL1PPPPz8g7empysrKVEBdt26dqqqe806v16vvvPNOyzY7d+5UAfXbb78NVDOD3tH9qKqqevrpp6u//e1vA9eoHigqKkp96aWX5Dz0QnMfqqqcg51RV1enZmRkqKtWrWrVb91xLsrI+lEcDgebN2/mzDPPbFmm0Wg488wz+fbbbwPYsp4nJyeH5ORkBg0axJVXXsn+/fsD3aQea+/evZSUlLQ6LyMiIpg0aZKcl520du1a4uPjGTp0KL/+9a85ePBgoJsU1GpqagCIjo4GYPPmzTidzlbn4rBhw+jXr5+ci8dxdD82e+ONN4iNjSUzM5O7774bm80WiOYFvaamJt58802sViuTJ0+W87ALju7DZnIOdsyiRYs4++yzW51z0D1/E3U+2UsvUlFRQVNTEwkJCa2WJyQk8PPPPweoVT3PpEmTeOWVVxg6dCjFxcXcf//9TJ06lezsbCwWS6Cb1+OUlJQAtHteNq8TJzZnzhwuvPBCBg4cSF5eHvfccw9z587l22+/RavVBrp5QcftdnPrrbcyZcoUMjMzAc+5aDAYiIyMbLWtnIvH1l4/AsyfP5/+/fuTnJzMtm3buOuuu9i1axfvv/9+AFsbXLZv387kyZOx2+2YzWY++OADRowYwdatW+U87KBj9SHIOdhRb775Jlu2bOH7779vs647/iZKsC78Yu7cuS33R40axaRJk+jfvz9vv/021157bQBbJvqyyy+/vOV+VlYWo0aNYvDgwaxdu5YZM2YEsGXBadGiRWRnZ8v1Jl46Vj9ef/31LfezsrJISkpixowZ5OXlMXjw4O5uZlAaOnQoW7dupaamhnfffZcFCxawbt26QDerRzlWH44YMULOwQ44cOAAv/3tb1m1ahUmkykgbZA0mKPExsai1WrbXMVbWlpKYmJigFrV80VGRjJkyBByc3MD3ZQeqfnck/PStwYNGkRsbKycl+24+eab+fTTT/niiy9ITU1tWZ6YmIjD4aC6urrV9nIutu9Y/dieSZMmAcj5eASDwUB6ejrjx4/n4YcfZvTo0Tz11FNyHnbCsfqwPXIOtrV582bKysoYN24cOp0OnU7HunXrePrpp9HpdCQkJPj9XJRg/SgGg4Hx48ezevXqlmVut5vVq1e3yvESnVNfX09eXh5JSUmBbkqPNHDgQBITE1udl7W1tWzcuFHOSy8UFBRw8OBBOS+PoKoqN998Mx988AFr1qxh4MCBrdaPHz8evV7f6lzctWsX+/fvl3PxCCfqx/Zs3boVQM7H43C73TQ2Nsp56IXmPmyPnINtzZgxg+3bt7N169aW24QJE7jyyitb7vv7XJQ0mHYsXryYBQsWMGHCBCZOnMiTTz6J1Wpl4cKFgW5aj/G73/2Oc889l/79+1NUVMS9996LVqvliiuuCHTTglZ9fX2r0Yy9e/eydetWoqOj6devH7feeisPPfQQGRkZDBw4kD/96U8kJyczb968wDU6yByvD6Ojo7n//vu56KKLSExMJC8vjzvvvJP09HRmz54dwFYHl0WLFrF06VI++ugjLBZLS85lREQEISEhREREcO2117J48WKio6MJDw/nlltuYfLkyZx88skBbn3wOFE/5uXlsXTpUs466yxiYmLYtm0bt912G6eddlqbsnB91d13383cuXPp168fdXV1LF26lLVr17JixQo5DzvoeH0o52DHWCyWVteaAISFhRETE9Oy3O/nok9qyvRCzzzzjNqvXz/VYDCoEydOVDds2BDoJvUol112mZqUlKQaDAY1JSVFveyyy9Tc3NxANyuoffHFFyrQ5rZgwQJVVT3lG//0pz+pCQkJqtFoVGfMmKHu2rUrsI0OMsfrQ5vNps6aNUuNi4tT9Xq92r9/f/VXv/qVWlJSEuhmB5X2+g9QX3755ZZtGhoa1JtuukmNiopSQ0ND1QsuuEAtLi4OXKOD0In6cf/+/eppp52mRkdHq0ajUU1PT1fvuOMOtaamJrANDyLXXHON2r9/f9VgMKhxcXHqjBkz1JUrV7asl/PwxI7Xh3IOdt3RJS/9fS4qqqqqvgn7hRBCCCGEEL4kOetCCCGEEEIEKQnWhRBCCCGECFISrAshhBBCCBGkJFgXQgghhBAiSEmwLoQQQgghRJCSYF0IIYQQQoggJcG6EEIIIYQQQUqCdSGEEEIIIYKUBOtCCCGEEEIEKQnWhRBCCCGECFISrAshhBBCCBGk/h+Phz8PREz5IAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 900x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from filterpy.kalman import FixedLagSmoother, KalmanFilter\n",
    "import numpy.random as random\n",
    "\n",
    "fls = FixedLagSmoother(dim_x=2, dim_z=1, N=8)\n",
    "\n",
    "fls.x = np.array([0., .5])\n",
    "fls.F = np.array([[1.,1.],\n",
    "                  [0.,1.]])\n",
    "\n",
    "fls.H = np.array([[1.,0.]])\n",
    "fls.P *= 200\n",
    "fls.R *= 5.\n",
    "fls.Q *= 0.001\n",
    "\n",
    "kf = KalmanFilter(dim_x=2, dim_z=1)\n",
    "kf.x = np.array([0., .5])\n",
    "kf.F = np.array([[1.,1.],\n",
    "                 [0.,1.]])\n",
    "kf.H = np.array([[1.,0.]])\n",
    "kf.P *= 200\n",
    "kf.R *= 5.\n",
    "kf.Q = Q_discrete_white_noise(dim=2, dt=1., var=0.001)\n",
    "\n",
    "N = 4 # size of lag\n",
    "\n",
    "nom =  np.array([t/2. for t in range (0, 40)])\n",
    "zs = np.array([t + random.randn()*5.1 for t in nom])\n",
    "\n",
    "for z in zs:\n",
    "    fls.smooth(z)\n",
    "    \n",
    "kf_x, _, _, _ = kf.batch_filter(zs)\n",
    "x_smooth = np.array(fls.xSmooth)[:, 0]\n",
    "\n",
    "\n",
    "fls_res = abs(x_smooth - nom)\n",
    "kf_res = abs(kf_x[:, 0] - nom)\n",
    "\n",
    "plt.plot(zs,'o', alpha=0.5, marker='o', label='zs')\n",
    "plt.plot(x_smooth, label='FLS')\n",
    "plt.plot(kf_x[:, 0], label='KF', ls='--')\n",
    "plt.legend(loc=4)\n",
    "\n",
    "print(f'standard deviation fixed-lag: {np.mean(fls_res):.3f}')\n",
    "print(f'standard deviation kalman: {np.mean(kf_res):.3f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0d3c101",
   "metadata": {},
   "source": [
    "在这里，我设置了“N=8”，这意味着我们将把 8 个未来的测量纳入我们的估计中。 一旦滤波器收敛，这为我们提供了一个非常平滑的估计，代价大约是标准卡尔曼滤波器计算量的 8 倍。 随意尝试更大和更小的“N”值。 我有点随意地选择了 8，不是出于任何理论上的考虑。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b288039a",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] H. Rauch, F. Tung, and C. Striebel. \"Maximum likelihood estimates of linear dynamic systems,\" *AIAA Journal*, **3**(8), pp. 1445-1450 (August 1965).\n",
    "\n",
    "[2] Dan Simon. \"Optimal State Estimation,\" John Wiley & Sons, 2006.\n",
    "\n",
    "http://arc.aiaa.org/doi/abs/10.2514/3.3166"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9c359d24",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
